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Ring system
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"Planet ring" redirects here. For other uses, see Planet Ring.
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The moons Prometheus (right) and Pandora orbit just inside and outside the F ring of Saturn, but only Prometheus is thought to function as a ring shepherd
A ring system is a disc or ring orbiting an astronomical object that is composed of solid material such as dust and moonlets, and is a common component of satellite systems around giant planets. A ring system around a planet is also known as a planetary ring system.
The most prominent and most famous planetary rings in the Solar System are those around Saturn, but the other three giant planets (Jupiter, Uranus, and Neptune) also have ring systems. Recent evidence suggests that ring systems may also be found around other types of astronomical objects, including minor planets, moons, and brown dwarfs.
Contents
[hide]
1 Ring systems of planets
1.1 Jupiter
1.2 Saturn
1.3 Uranus
1.4 Neptune
2 Rings systems of minor planets and moons
3 Rings around exoplanets
4 Visual comparison
5 References
6 External links
Ring systems of planets[edit]
The ring swirling around Saturn consists of chunks of ice and dust. The little dark spot on Saturn is the shadow from Saturn's moon Enceladus.
There are three ways that thicker planetary rings (the rings around planets) have been proposed to have formed: from material of the protoplanetary disk that was within the Roche limit of the planet and thus could not coalesce to form moons, from the debris of a moon that was disrupted by a large impact, or from the debris of a moon that was disrupted by tidal stresses when it passed within the planet's Roche limit. Most rings were thought to be unstable and to dissipate over the course of tens or hundreds of millions of years, but it now appears that Saturn's rings might be quite old, dating to the early days of the Solar System.[1]
Fainter planetary rings can form as a result of meteoroid impacts with moons orbiting around the planet or, in case of Saturn's E-ring, the ejecta of cryovolcanic material.[2][3]
The composition of ring particles varies; they may be silicate or icy dust. Larger rocks and boulders may also be present, and in 2007 tidal effects from eight 'moonlets' only a few hundred meters across were detected within Saturn's rings. The maximum size of a ring particle is determined by the specific strength of the material it is made of, its density, and the tidal force at its altitude. The tidal force is proportional to the average density inside the radius of the ring, or to the mass of the planet divided by the radius of the ring cubed. It is also inversely proportional to the square of the orbital period of the ring.
Sometimes rings will have "shepherd" moons, small moons that orbit near the inner or outer edges of rings or within gaps in the rings. The gravity of shepherd moons serves to maintain a sharply defined edge to the ring; material that drifts closer to the shepherd moon's orbit is either deflected back into the body of the ring, ejected from the system, or accreted onto the moon itself.
It is also predicted that Phobos, a moon of Mars, will break up and form into a planetary ring in about 50 million years, because its low orbit with an orbital period that is shorter than a Martian day is decaying due to tidal deceleration.[4][5]
Jupiter[edit]
Main article: Rings of Jupiter
Jupiter's ring system was the third to be discovered, when it was first observed by the Voyager 1 probe in 1979,[6] and was observed more thoroughly by the Galileo orbiter in the 1990s.[7] Its four main parts are a faint thick torus known as the "halo"; a thin, relatively bright main ring; and two wide, faint "gossamer rings".[8] The system consists mostly of dust.[6][9]
Saturn[edit]
Main article: Rings of Saturn
Saturn's rings are the most extensive ring system of any planet in the Solar System, and thus have been known to exist for quite some time. Galileo Galilei first observed them in 1610, but they were not accurately described as a disk around Saturn until Christiaan Huygens did so in 1655.[10] With help from the NASA/ESA/ASI Cassini mission, a further understanding of the ring formation and active movement was understood.[11] The rings are not a series of tiny ringlets as many think, but are more of a disk with varying density.[12] They consist mostly of water ice and trace amounts of rock, and the particles range in size from micrometers to meters.[13]
Uranus[edit]
Main article: Rings of Uranus
Uranus' ring system lies between the level of complexity of Saturn's vast system and the simpler systems around Jupiter and Neptune. They were discovered in 1977 by James L. Elliot, Edward W. Dunham, and Jessica Mink.[14] In the time between then and 2005, observations by Voyager 2[15] and the Hubble Space Telescope[16] led to a total of 13 distinct rings being identified, most of which are opaque and only a few kilometers wide. They are dark and likely consist of water ice and some radiation-processed organics. The relative lack of dust is due to aerodynamic drag from the extended exosphere-corona of Uranus.
Neptune[edit]
Main article: Rings of Neptune
The system around Neptune consists of five principal rings that, at their densest, are comparable to the low-density regions of Saturn's rings. However, they are faint and dusty, much more similar in structure to those of Jupiter. The very dark material that makes up the rings are likely organics processed by radiation, like in the rings of Uranus.[17] 20 to 70 percent of the rings are dust, a relatively high proportion.[17] Hints of the rings were seen for decades prior to their conclusive discovery by Voyager 2 in 1989.
Rings systems of minor planets and moons[edit]
Reports in March 2008[18][19][20] suggested that Saturn's moon Rhea may have its own tenuous ring system, which would make it the only moon known to have a ring system. A later study published in 2010 revealed that imaging of Rhea by the Cassini spacecraft was inconsistent with the predicted properties of the rings, suggesting that some other mechanism is responsible for the magnetic effects that had led to the ring hypothesis.[21]
10199 Chariklo, a centaur, was the first minor planet discovered to have rings. It has two rings, perhaps due to a collision that caused a chain of debris to orbit it. The rings were discovered when astronomers observed Chariklo passing in front of the star UCAC4 248-108672 on June 3, 2013 from seven locations in South America. While watching, they saw two dips in the star's apparent brightness just before and after the occultation. Because this event was observed at multiple locations, the conclusion that the dip in brightness was in fact due to rings is unanimously the leading hypothesis. The observations revealed what is likely a 19-kilometer (12-mile)-wide ring system that is about 1,000 times closer than the Moon is to Earth. In addition, astronomers suspect there could be a moon orbiting amidst the ring debris. If these rings are the leftovers of a collision as astronomers suspect, this would give fodder to the idea that moons (such as the Moon) form through collisions of smaller bits of material. Chariklo's rings have not been officially named, but the discoverers have nicknamed them Oiapoque and Chuí, after two rivers near the northern and southern ends of Brazil.[22]
A second centaur, 2060 Chiron, is also suspected to have a pair of rings.[23][24] Based on stellar-occultation data that were initially interpreted as resulting from jets associated with Chiron's comet-like activity, the rings are proposed to be 324 (± 10) km in radius. Their changing appearance at different viewing angles can explain the long-term variation in Chiron's brightness over time.[24]
Ring systems may form around centaurs when they are tidally disrupted in a close encounter (within 0.4 to 0.8 times the Roche limit) with a giant planet. (By definition, a centaur is a minor planet whose orbit crosses the orbit(s) of one or more giant planets.) For a differentiated body approaching a giant planet at an initial relative velocity of 3−6 km/s with an initial rotational period of 8 hours, a ring mass of 0.1−10% of the centaur's mass is predicted. Ring formation from an undifferentiated body is less likely. The rings would be composed mostly or entirely of material from the parent body's icy mantle. After forming, the ring would spread laterally, leading to satellite formation from whatever portion of it spreads beyond the centaur's Roche Limit. Satellites could also form directly from the disrupted icy mantle. This formation mechanism predicts that roughly 10% of centaurs will have experienced potentially ring-forming encounters with giant planets.[25]
A ring around Haumea, a dwarf planet and resonant Kuiper belt member, was revealed by a stellar occultation observed on 21 January 2017. This makes it the first trans-Neptunian object found to have a ring system.[26][27] The ring has a radius of about 2,287 km, a width of ≈70 km and an opacity of 0.5.[27] The ring plane coincides with Haumea’s equator and the orbit of its larger, outer moon Hi’iaka[27] (which has a semimajor axis of ≈25,657 km). The ring is close to the 3:1 resonance with Haumea's rotation, which is located at a radius of 2,285 ± 8 km.[27] It is well within Haumea's Roche limit, which would lie at a radius of about 4,400 km if Haumea were spherical (being nonspherical pushes the limit out farther).[27]
It had previously been theorized by some astronomers that Pluto might have a ring system.[28] However, this possibility has been ruled out by New Horizons, which would have detected any such ring system.
Rings around exoplanets[edit]
Because all giant planets of the Solar System have rings, the existence of exoplanets with rings is plausible. Although particles of ice, the material that is predominant in the rings of Saturn, can only exist around planets beyond the frost line, within this line rings consisting of rocky material can be stable in the long term.[29] Such ring systems can be detected for planets observed by the transit method by additional reduction of the light of the central star if their opacity is sufficient. As of January 2015, no such observations are known.
A sequence of occultations of the star 1SWASP J140747.93-394542.6 observed in 2007 over 56 days was interpreted as a transit of a ring system of a (not directly observed) substellar companion dubbed “J1407b”.[30] This ring system is attributed a radius of about 90 million km (about 200 times that of Saturn's rings). In press releases, the term super-Saturn was dubbed.[31] However, the age of this stellar system is only about 16 million years, which suggests that this structure, if real, is more like a protoplanetary disk rather than a stable ring system in an evolved planetary system.
Fomalhaut b was found to be large and unclearly defined when detected in 2008. This may either be due to a cloud of dust attracted from the dust disc of the star, or a possible ring system.[32]
Visual comparison[edit]
A Galileo image of Jupiter's main ring.
A Cassini mosaic of Saturn's rings.
A Voyager 2 image of Uranus's rings.
A pair of Voyager 2 images of Neptune's rings.
References[edit]
Jump up ^ "Saturn's Rings May Be Old Timers". NASA (News Release 2007-149). December 12, 2007. Retrieved 2008-04-11.
Jump up ^ Spahn, F.; et al. (2006). "Cassini Dust Measurements at Enceladus and Implications for the Origin of the E Ring" (PDF). Science. 311 (5766): 1416–8. Bibcode:2006Sci...311.1416S. doi:10.1126/science.1121375. PMID 16527969.
Jump up ^ Porco, C. C.; Helfenstein, P.; Thomas, P. C.; Ingersoll, A. P.; Wisdom, J.; West, R.; Neukum, G.; Denk, T.; Wagner, R. (10 March 2006). "Cassini Observes the Active South Pole of Enceladus". Science. 311 (5766): 1393–1401. Bibcode:2006Sci...311.1393P. doi:10.1126/science.1123013. PMID 16527964.
Jump up ^ Holsapple, K. A. (December 2001). "Equilibrium Configurations of Solid Cohesionless Bodies". Icarus. 154 (2): 432–448. Bibcode:2001Icar..154..432H. doi:10.1006/icar.2001.6683.
Jump up ^ Gürtler, J. & Dorschner, J: "Das Sonnensystem", Barth (1993), ISBN 3-335-00281-4
^ Jump up to: a b Smith, Bradford A.; Soderblom, Laurence A.; Johnson, Torrence V.; Ingersoll, Andrew P.; Collins, Stewart A.; Shoemaker, Eugene M.; Hunt, G. E.; Masursky, Harold; Carr, Michael H. (1979-06-01). "The Jupiter System Through the Eyes of Voyager 1". Science. 204 (4396): 951–972. Bibcode:1979Sci...204..951S. doi:10.1126/science.204.4396.951. ISSN 0036-8075. PMID 17800430.
Jump up ^ Ockert-Bell, Maureen E.; Burns, Joseph A.; Daubar, Ingrid J.; Thomas, Peter C.; Veverka, Joseph; Belton, M. J. S.; Klaasen, Kenneth P. (1999-04-01). "The Structure of Jupiter's Ring System as Revealed by the Galileo Imaging Experiment". Icarus. 138 (2): 188–213. Bibcode:1999Icar..138..188O. doi:10.1006/icar.1998.6072.
Jump up ^ Esposito, Larry W. (2002-01-01). "Planetary rings". Reports on Progress in Physics. 65 (12): 1741. Bibcode:2002RPPh...65.1741E. doi:10.1088/0034-4885/65/12/201. ISSN 0034-4885.
Jump up ^ Showalter, Mark R.; Burns, Joseph A.; Cuzzi, Jeffrey N.; Pollack, James B. (1987-03-01). "Jupiter's ring system: New results on structure and particle properties". Icarus. 69 (3): 458–498. Bibcode:1987Icar...69..458S. doi:10.1016/0019-1035(87)90018-2.
Jump up ^ "Historical Background of Saturn's Rings". www.solarviews.com. Retrieved 2016-06-15.
Jump up ^ "Cassini - In Depth | Missions - NASA Solar System Exploration". NASA Solar System Exploration. Retrieved 2017-02-13.
Jump up ^ Tiscareno, Matthew S. (2013-01-01). Oswalt, Terry D.; French, Linda M.; Kalas, Paul, eds. Planetary Rings. Springer Netherlands. pp. 309–375. doi:10.1007/978-94-007-5606-9_7. ISBN 9789400756052.
Jump up ^ Porco, Carolyn. "Questions about Saturn's rings". CICLOPS web site. Retrieved 2012-10-05.
Jump up ^ Elliot, J. L.; Dunham, E.; Mink, D. (1977-05-26). "The rings of Uranus". Nature. 267 (5609): 328–330. Bibcode:1977Natur.267..328E. doi:10.1038/267328a0.
Jump up ^ Smith, B. A.; Soderblom, L. A.; Beebe, R.; Bliss, D.; Boyce, J. M.; Brahic, A.; Briggs, G. A.; Brown, R. H.; Collins, S. A. (1986-07-04). "Voyager 2 in the Uranian System: Imaging Science Results". Science. 233 (4759): 43–64. Bibcode:1986Sci...233...43S. doi:10.1126/science.233.4759.43. ISSN 0036-8075. PMID 17812889.
Jump up ^ Showalter, Mark R.; Lissauer, Jack J. (2006-02-17). "The Second Ring-Moon System of Uranus: Discovery and Dynamics". Science. 311 (5763): 973–977. Bibcode:2006Sci...311..973S. doi:10.1126/science.1122882. ISSN 0036-8075. PMID 16373533.
^ Jump up to: a b Smith, B. A.; Soderblom, L. A.; Banfield, D.; Barnet, C; Basilevsky, A. T.; Beebe, R. F.; Bollinger, K.; Boyce, J. M.; Brahic, A. (1989-12-15). "Voyager 2 at Neptune: Imaging Science Results". Science. 246 (4936): 1422–1449. Bibcode:1989Sci...246.1422S. doi:10.1126/science.246.4936.1422. ISSN 0036-8075. PMID 17755997.
Jump up ^ http://www.nasa.gov/mission_pages/cassini/media/rhea20080306.html NASA – Saturn's Moon Rhea Also May Have Rings
Jump up ^ Jones, G. H.; et al. (2008-03-07). "The Dust Halo of Saturn's Largest Icy Moon, Rhea". Science. 319 (5868): 1380–1384. Bibcode:2008Sci...319.1380J. doi:10.1126/science.1151524. PMID 18323452.
Jump up ^ Lakdawalla, E. (2008-03-06). "A Ringed Moon of Saturn? Cassini Discovers Possible Rings at Rhea". The Planetary Society web site. Planetary Society. Retrieved 2008-03-09.
Jump up ^ Tiscareno, Matthew S.; Burns, Joseph A.; Cuzzi, Jeffrey N.; Hedman, Matthew M. (2010). "Cassini imaging search rules out rings around Rhea". Geophysical Research Letters. 37 (14): L14205. arXiv:1008.1764  . Bibcode:2010GeoRL..3714205T. doi:10.1029/2010GL043663.
Jump up ^ "Surprise! Asteroid Hosts A Two-Ring Circus Above Its Surface". Universe Today. March 2014.
Jump up ^ Lakdawalla, E. (2015-01-27). "A second ringed centaur? Centaurs with rings could be common". Planetary Society. Retrieved 2015-01-31.
^ Jump up to: a b Ortiz, J.L.; Duffard, R.; Pinilla-Alonso, N.; Alvarez-Candal, A.; Santos-Sanz, P.; Morales, N.; Fernández-Valenzuela, E.; Licandro, J.; Campo Bagatin, A.; Thirouin, A. (2015). "Possible ring material around centaur (2060) Chiron". Astronomy & Astrophysics. 576: A18. arXiv:1501.05911  . Bibcode:2015yCat..35760018O. doi:10.1051/0004-6361/201424461.
Jump up ^ Hyodo, R.; Charnoz, S.; Genda, H.; Ohtsuki, K. (2016-08-29). "Formation of Centaurs' Rings Through Their Partial Tidal Disruption During Planetary Encounters". The Astrophysical Journal. 828 (1): L8. arXiv:1608.03509  . Bibcode:2016ApJ...828L...8H. doi:10.3847/2041-8205/828/1/L8.
Jump up ^ Sickafoose, A. A. (2017). "Astronomy: Ring detected around a dwarf planet". Nature. 550 (7675): 197–198. Bibcode:2017Natur.550..197S. doi:10.1038/550197a.
^ Jump up to: a b c d e Ortiz, J. L.; Santos-Sanz, P.; Sicardy, B.; et al. (2017). "The size, shape, density and ring of the dwarf planet Haumea from a stellar occultation". Nature. 550 (7675): 219–223. Bibcode:2017Natur.550..219O. doi:10.1038/nature24051.
Jump up ^ Steffl, Andrew J.; Stern, S. Alan (2007). "First Constraints on Rings in the Pluto System". The Astronomical Journal. 133 (4): 1485–1489. arXiv:astro-ph/0608036  . Bibcode:2007AJ....133.1485S. doi:10.1086/511770.
Jump up ^ Hilke E. Schlichting, Philip Chang (2011). "Warm Saturns: On the Nature of Rings around Extrasolar Planets that Reside Inside the Ice Line". Astrophysical Journal. 734 (2): 117. arXiv:1104.3863  . Bibcode:2011ApJ...734..117S. doi:10.1088/0004-637X/734/2/117.
Jump up ^ Matthew A. Kenworthy, Eric E. Mamajek (2015). "Modeling giant extrasolar ring systems in eclipse and the case of J1407b: sculpting by exomoons?". The Astrophysical Journal. 800 (2): 126. arXiv:1501.05652  . Bibcode:2015ApJ...800..126K. doi:10.1088/0004-637X/800/2/126.
Jump up ^ Rachel Feltman (2015-01-26). "This planet's rings make Saturn look puny". The Washington Post. Retrieved 2015-01-27.
Jump up ^ arXiv:0811.1994 [astro-ph], available at https://arxiv.org/abs/0811.1994, by Kalas, P. et al. Accessed 4th Feb. 2018
External links[edit]
Wikimedia Commons has media related to Planetary rings.
USGS/IAU Ring and Ring Gap Nomenclature
Everything a Curious Mind Should Know About Planetary Ring Systems with Dr Mark Showalter, Bridging the Gaps: A Portal for Curious Minds
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text:
One pound (British coin)
From Wikipedia, the free encyclopedia
Jump to: navigation, search
"£1" redirects here. For other uses, see List of £1.
One pound
United Kingdom
Value
1 pound sterling
Mass
(Round) 9.5 g
(12-sided) 8.75 g
Diameter
(Round) 22.5 mm
(12-sided) 23.03-23.43 mm
Thickness
(Round) 3.15 mm
(12-sided) 2.8 mm
Edge
(Round) Milled, with incuse lettering
(12-sided) Alternately milled and plain
Composition
(Round) Nickel-brass
(70% Cu, 24.5% Zn, and 5.5% Ni)
(12-sided, outer ring)
Nickel-brass
(76% Cu, 20% Zn, and 4% Ni)
(12-sided, inner circle)
Nickel-plated alloy
Obverse
Design
Queen Elizabeth II
Designer
Jody Clark
Design date
2015 (round)
2016 (12-sided)
Reverse
Design
The shield of the Royal Coat of Arms (round)
Rose, leek, thistle, and shamrock encircled by a coronet (12-sided)
Designer
Matthew Dent (round)
David Pearce (12-sided)
Design date
2008 (round)
2016 (12-sided)
The British one pound (£1) coin is a denomination of the pound sterling. Its obverse bears the Latin engraving D G REG “Dei Gratia Regina” meaning, “By the grace of God, Queen” and F D meaning Fidei defensor,[1] Defender of the Faith.[2] It has featured the profile of Queen Elizabeth II since the coin's introduction on 21 April 1983.[3] Four different portraits of the Queen have been used, with the latest design by Jody Clark being introduced in 2015. The design on the reverse side of the new 2017 coin features four emblems to represent each of the nations of the United Kingdom – the English rose, the leek for Wales, the Scottish thistle, and the shamrock for Northern Ireland – emerging from a single stem within a crown.
The £1 coin replaced the Bank of England £1 note, which ceased to be issued at the end of 1984 and was removed from circulation on 11 March 1988, though still redeemable at the Bank's offices, like all English banknotes. One-pound notes continue to be issued in Jersey, Guernsey and the Isle of Man, and by the Royal Bank of Scotland, but the pound coin is much more widely used.
Since 28 March 2017, two versions of the one pound coin have been in circulation – the original round design and a new dodecagonal (12-sided) design.[4] As of March 2014 there were an estimated 1,553 million round £1 coins in circulation,[5] of which the Royal Mint estimated in 2014 that 3.04% (i.e. about 47 million) were counterfeit.[6][7] In an effort to counter this, the Royal Mint introduced the new 12-sided coin, which is bimetallic like the current £2 coin, and features an undisclosed hidden security feature called 'iSIS' (Integrated Secure Identification Systems).[8][9] The round pound will remain in circulation until 15 October 2017. After that date, the older coin can only be redeemed at banks.[10]
Contents
[hide]
1 Design
2 Mintage figures
2.1 Round coin
2.2 12-sided coin
3 Counterfeiting
4 Other pound coins in circulation
5 Further reading
6 See also
7 References
8 External links
Design[edit]
To date, five different obverses have been used. For the first three of these, the inscription was ELIZABETH II D.G.REG.F.D. 2013,[11] where 2013 is replaced by the year of minting. The fourth design, unveiled in March 2015,[12] expanded the inscription slightly to ELIZABETH II DEI.GRA.REG.FID.DEF. 2015. The fifth design, introduced in March 2017, reverted to D.G.REG.F.D.
In summary:
In 1983 and 1984 the portrait of Queen Elizabeth II by Arnold Machin appeared on the obverse,[13] in which the Queen wears the 'Girls of Great Britain and Ireland' Tiara.
Between 1985 and 1997 the portrait by Raphael Maklouf was used,[13] in which the Queen wears the George IV State Diadem.
Between 1998 and 2015 the portrait by Ian Rank-Broadley was used,[13] again featuring the tiara, with a signature-mark IRB below the portrait.
In 2015 the portrait by Jody Clark was introduced,[14] in which the Queen wears the George IV State Diadem,[15] with a signature-mark JC below the portrait.
In August 2005 the Royal Mint launched a competition to find new reverse designs for all circulating coins apart from the £2 coin.[16] The winner, announced in April 2008, was Matthew Dent, whose designs were gradually introduced into the circulating British coinage from mid-2008.[17] The designs for the 1p, 2p, 5p, 10p, 20p and 50p coins depict sections of the Royal Shield that form the whole shield when placed together. The shield in its entirety is featured on the £1 coin. The coin's obverse remains unchanged.
The design of the reverse of the coin was changed each year from 1983 to 2008 to show, in turn, an emblem representing the UK, Scotland, Wales, Northern Ireland, and England, together with an appropriate edge inscription. This edge inscription may frequently be "upside-down" (when obverse is facing upward).[18] Since 2008, national-based designs have still been minted, but alongside the new standard version, and no longer in strict rotation. The inscription ONE POUND appears on all reverse designs.
In common with non-commemorative £2 coins, the £1 coin (except 2004–07 and the 2010–11 'capital cities' designs) has a mint mark: a small crosslet found on the milled edge that represents Llantrisant in South Wales, where the Royal Mint has been based since 1968.[19]
The reverse of the new 12-sided bimetallic pound coin, introduced on 28 March 2017,[4] was chosen by a public design competition.[20] The competition to design the reverse of this coin was opened in September 2014.[21] It was won in March 2015 by 15-year-old David Pearce from Walsall, and unveiled by Chancellor George Osborne during his Budget announcement. The design features a rose, leek, thistle and shamrock bound by a crown.[12] The current round pound will remain legal tender alongside the new 12-sided design until 15 October 2017.[4] After said date, the older round coin will only be redeemable at banks. The round pound will remain legal tender on the Isle of Man.[22]
Mintage figures[edit]
Round coin[edit]
Images: Royal Mint
Year
Design
Nation represented
Edge inscription
Translation
Mintage[23]
1983 Ornamental royal arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 443,053,510
1984 Thistle and royal diadem Scotland NEMO ME IMPUNE LACESSIT No one attacks me with impunity 146,256,501
1985 Leek and royal diadem Wales PLEIDIOL WYF I'M GWLAD True am I to my country 228,430,749
1986 Flax plant and royal diadem Northern Ireland DECUS ET TUTAMEN An ornament and a safeguard 10,409,501
1987 Oak tree and royal diadem England DECUS ET TUTAMEN An ornament and a safeguard 39,298,502
1988 Crown over the Royal Coat of Arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 7,118,825
1989 Thistle and royal diadem Scotland NEMO ME IMPUNE LACESSIT No one attacks me with impunity 70,580,501
1990 Leek and royal diadem Wales PLEIDIOL WYF I'M GWLAD True am I to my country 97,269,302
1991 Flax plant and royal diadem Northern Ireland DECUS ET TUTAMEN An ornament and a safeguard 38,443,575
1992 Oak tree and royal diadem England DECUS ET TUTAMEN An ornament and a safeguard 36,320,487
1993 Ornamental royal arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 114,744,500
1994 Lion rampant within a double tressure flory counter-flory Scotland NEMO ME IMPUNE LACESSIT No one attacks me with impunity 29,752,525
1995 Dragon passant Wales PLEIDIOL WYF I'M GWLAD True am I to my country 34,503,501
1996 Celtic cross, Broighter collar and pimpernel Northern Ireland DECUS ET TUTAMEN An ornament and a safeguard 89,886,000
1997 Three lions passant guardant England DECUS ET TUTAMEN An ornament and a safeguard 57,117,450
1998 Ornamental royal arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard not circulated
1999 Lion rampant within a double tressure flory counter-flory Scotland NEMO ME IMPUNE LACESSIT No one attacks me with impunity not circulated
2000 Dragon passant Wales PLEIDIOL WYF I'M GWLAD True am I to my country 109,496,500
2001 Celtic cross, Broighter collar and pimpernel Northern Ireland DECUS ET TUTAMEN An ornament and a safeguard 63,968,065
2002 Three lions passant guardant England DECUS ET TUTAMEN An ornament and a safeguard 77,818,000
2003 Ornamental royal arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 61,596,500
2004 Forth Railway Bridge surrounded by railway tracks Scotland An incuse decorative feature symbolising bridges and pathways N/A 39,162,000
2005 Menai Suspension Bridge surrounded by railing and stanchions Wales 99,429,500
2006 Egyptian Arch Railway Bridge surrounded by railway station canopy dags Northern Ireland 38,938,000
2007 Gateshead Millennium Bridge surrounded by struts England 26,180,160
2008 Ornamental royal arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 3,910,000
2008 The shield from the Royal Coat of Arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 43,827,300
2009 The shield from the Royal Coat of Arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 27,625,600
2010 The shield from the Royal Coat of Arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 57,120,000
2010 Coat of arms of the City of London England DOMINE DIRIGE NOS Lord, guide us 2,635,000
2010 Coat of arms of Belfast Northern Ireland PRO TANTO QUID RETRIBUAMUS For so much, what shall we give in return? 6,205,000
2011 The shield from the Royal Coat of Arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 25,415,000
2011 Coat of arms of Cardiff Wales Y DDRAIG GOCH DDYRY CYCHWYN The red dragon will give the lead 1,615,000
2011 Coat of arms of Edinburgh Scotland NISI DOMINUS FRUSTRA In vain without the Lord 935,000
2012 The shield from the Royal Coat of Arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 35,700,030
2013 The shield from the Royal Coat of Arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 13,090,500
2013 Oak and rose England DECUS ET TUTAMEN An ornament and a safeguard 5,270,000
2013 Leek and daffodil Wales PLEIDIOL WYF I'M GWLAD True am I to my country 5,270,000
2014 Shamrock and flax plant[24] Northern Ireland DECUS ET TUTAMEN An ornament and a safeguard 5,780,000
2014 Thistle and bluebell[24] Scotland NEMO ME IMPUNE LACESSIT No one attacks me with impunity 5,185,000
2014 The shield from the Royal Coat of Arms United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 79,305,200
2015 The shield from the Royal Coat of Arms (4th portrait)[25] United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 29,580,000
2015 The Royal Coat of Arms (5th portrait)[26] United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 131,250,000[26]
2016 The shield from the Royal Coat of Arms (5th portrait)[27][28] United Kingdom DECUS ET TUTAMEN An ornament and a safeguard 30,000 (only in BU sets)
2016 Four heraldic beasts[29] United Kingdom DECUS ET TUTAMEN An ornament and a safeguard not circulated
All years except 1998 and 1999 have been issued into circulation, although the number issued has varied enormously – 1983, 1984 and 1985 in particular had large mintages to facilitate the changeover from paper notes, while some years such as 1988 are only rarely seen (although 1988 is more noticeable as it has a unique reverse). Production since 1997 has been reduced, thanks to the introduction of the circulating two pound coin.
The final round coins minted for 2016 did not enter circulation, as they were only available through commemorative sets.[30] These were the shield from the Royal Coat of Arms by Matthew Dent, and a design by Gregory Cameron, Bishop of St Asaph, of four heraldic beasts.[29][31]
12-sided coin[edit]
Year
Design
Nation represented
Mintage[23]
2016 Nations of the Crown United Kingdom 300,000,000 (initial launch in March 2017)[32]
2017 Nations of the Crown United Kingdom TBA
Counterfeiting[edit]
Royal Mint surveys estimate the proportion of counterfeit £1 coins in circulation. This was estimated at 3.04% in 2013, a rise from 2.74%.[6][7] The figure previously announced in 2012 was 2.86%, following the prolonged rise from 0.92% in 2002–2003 to 0.98% in 2004, 1.26% in 2005, 1.69% in 2006, 2.06% in 2007, 2.58% in 2008, 2.65% in 2009, 3.07% in 2010 and 3.09% in 2011.[33][34] Figures have generally been reported in the following year; in 2008 (as reported in 2009), the highest levels of counterfeits were in Northern Ireland (3.6%) and the South East and London (2.97%), with the lowest being in Northwest England.[35][36][37] Coin testing companies estimated in 2009 that the actual figure was about twice the Mint's estimate, suggesting that the Mint was underplaying the figures so as not to undermine confidence in the coin.[38] It is illegal to pass on counterfeit currency knowingly; the official advice is to hand it in, with details of where received, to the police, who will retain it and investigate.[39][40] One article suggested "given that fake coins are worthless, you will almost certainly be better off not even looking".[38] The recipient has recourse against the supplier, as in any such case.
Counterfeits are put into circulation by dishonest people, then circulated inadvertently by others who are unaware; in many cases banks do not check, and circulate counterfeits. A 2011 BBC television programme withdrew 1,000 £1 coins from each of five major banks and found that each batch contained between 32 and 38 counterfeits; the Mint estimated that about 31 per 1,000 £1 coins were counterfeit.[39] Some of the counterfeits were found by automated machinery, others could be detected only by expert visual inspection.
In July 2010, following speculation that the Royal Mint would have to consider replacing £1 coins with a new design because of the fakes, bookmakers Paddy Power offered odds of 6/4 (bet £4 to win £6, plus the £4 stake back; decimal odds of 2.5), that the £1 coin would be removed from circulation.[36][41]
Real and fake pound coin, showing poor-quality edge inscription and milling
Some counterfeits are of poor quality, with obviously visible differences (less sharply defined, lacking intricate details, edge milling and markings visibly wrong). Many better counterfeits can be detected by comparing the orientation of the obverse and reverse—they always match in genuine coins, but very often not in counterfeits.[39][40] The design on the reverse must be correct for the stamped year (e.g., a 1996 coin should have a Celtic cross).[42] It is difficult to manufacture coins with properly-produced edges; the milling (grooves) may be incomplete or poor and the inscription (often "DECUS ET TUTAMEN") may be poorly produced and sometimes in the wrong typeface.[39] A shiny coin with less wear than its date suggests is also suspect, although it may be a genuine coin that has rarely been used.[40]
Counterfeit coins are made by different processes including casting, stamping, electrotyping, and copying with a pantograph or spark erosion.[43] In a 2009 survey, 99% of fake £1 coins found in cash centres were made of a nickel-brass, of which three fifths contained some lead and a fifth were of a very similar alloy to that used by the Royal Mint. The remaining 1% were made of simple copper-zinc brass, or lead or tin, or both.[44] Those made of lead or tin may have a gold-coloured coating; counterfeits made of acrylic plastic containing metal powder to increase weight have occasionally been found.[43]
The final "round coins" were minted in December 2015; the replacement, a new 12-sided design, was introduced in 2017.[45] The coin has a 12-edged shape, similar to the pre-decimal brass threepence coin; it has roughly the same size as the previous £1 coin, and is bi-metallic like the current £2 coin. The new design is intended to make counterfeiting more difficult, and also has an undisclosed hidden security feature called "iSIS" (Integrated Secure Identification Systems).[20][46]
Current two-pound coins are made from two metals of different colour, and are much harder to counterfeit; counterfeited coins are often easily seen to be the wrong colour.
Other pound coins in circulation[edit]
Also legally circulating but not legal tender in the UK, are some £1 coins of British Crown Dependencies, Gibraltar and UK South Atlantic Overseas Territories, being of the same size and composition as their UK equivalent and mostly bearing the same portraits of the UK monarch (as with most other coins of the same territories).[47][48]
Further reading[edit]
In an April 1993 The New Yorker article 'Real Britannia', Julian Barnes describes the meetings to choose the 1994–1997 reverse designs.[49] This is reprinted in his book Letters from London as 'Britannia's New Bra Size'.
See also[edit]
Numismatics portal
Banknotes of the pound sterling
Coin counterfeiting
Coins of the pound sterling
References[edit]
Jump up ^ "No. 39873". The London Gazette (11th supplement). 26 May 1953. p. 3023. Proclamation of 28 May 1953 made in accordance with the Royal Titles Act 1953.
Jump up ^ "Project Britain-British Coins". 2013. Retrieved 2016-10-27.
Jump up ^ "One Pound Coin". Royal Mint. Retrieved 22 November 2016.
^ Jump up to: a b c "New 12-sided pound coin to enter circulation in March". BBC News. 1 January 2017. Retrieved 2 January 2017.
Jump up ^ "Mintage Figures". Royal Mint. Retrieved 28 December 2015.
^ Jump up to: a b "£1 Counterfeit Coins". royalmint.com. Retrieved 1 September 2014.
^ Jump up to: a b "How can I spot a fake £1 coin?". London: The Telegraph. 19 March 2014.
Jump up ^ "New pound coin: Firms told to prepare for redesign". BBC News. 2016-10-31. Retrieved 2016-10-31.
Jump up ^ "Specification of the £1 coin: a technical consultation" (PDF). HM Treasury. September 2014.
Jump up ^ Giedroyc, Richard (23 May 2017). "‘Most secure coin in world’ launched". numismaticsnews.net. Retrieved 24 May 2017.
Jump up ^ Clayton, Tony. "Decimal Coins of the UK – Bronze". tclayton.demon.co.uk. Retrieved 24 May 2006.
^ Jump up to: a b Allen, Katie (17 March 2015). "New 12-sided pound coin to be unveiled ahead of budget announcement". The Guardian. Retrieved 18 March 2015.
^ Jump up to: a b c "1p Coin". British Royal Mint. Archived from the original on 27 April 2006. Retrieved 23 May 2006.
Jump up ^ "Royal Mint unveils new coinage portrait of the Queen". BBC News. 2 March 2015. Retrieved 18 March 2015.
Jump up ^ "The reveal of the Queen's fifth coin portrait". Royal Mint. 2 March 2015. Retrieved 18 March 2015.
Jump up ^ "Royal Mint seeks new coin designs", BBC News, 17 August 2005
Jump up ^ "Royal Mint unveils new UK coins", dofonline.co.uk, 2 April 2008
Jump up ^ Royal Mint. "Why does the edge inscription on the £2 and £1 coins sometimes appear "upside down"?". Retrieved 2 November 2016.
Jump up ^ "History of the Royal Mint". 24carat.co.uk. Retrieved 9 April 2008.
^ Jump up to: a b "The New One Pound Coin". royalmint.com. 19 March 2014. Retrieved 19 March 2014.
Jump up ^ New One Pound Coin Royal Mint
Jump up ^ "Manx round pound coins to remain 'legal tender'". BBC News. 7 February 2017. Retrieved 6 October 2017.
^ Jump up to: a b "Decimal coins issued £2 – 20p". The Royal Mint Limited. 2016. Retrieved 16 June 2016.
^ Jump up to: a b "New coin designs for 2014 unveiled by The Royal Mint". BBC News. 31 December 2013. Retrieved 21 January 2014.
Jump up ^ "Decimal coins issued up to 31 December 2015 £2 - 20p". The Royal Mint. Retrieved 2017-03-28.
^ Jump up to: a b "Decimal coins issued up to 31 December 2015 £2 - 20p". The Royal Mint. Retrieved 2017-08-06.
Jump up ^ "2016 One Pound | Check Your Change". www.checkyourchange.co.uk. Retrieved 2017-03-28.
Jump up ^ "2013 Dated UK Collector Coin Sales". The Royal Mint. Retrieved 28 March 2017.
^ Jump up to: a b "The Last Round Pound 2016 United Kingdom £1 Brilliant Uncirculated Coin". The Royal Mint. Retrieved 2016-06-09.
Jump up ^ "2016 One Pound". www.checkyourchange.co.uk. Retrieved 2017-03-28.
Jump up ^ Powell, Anna (16 May 2016). "Behind the design: the last 'round pound'". The Royal Mint blog. The Royal Mint. Retrieved 19 October 2016.
Jump up ^ Anthony, Sebastian (28 March 2017). "New “impossible” to fake £1 coin enters circulation today". Ars Technica. Retrieved 3 April 2017.
Jump up ^ Clive Kahn (17 December 2012). "43.5 Million Fake Pound Coins in Circulation". BusinessReport.
Jump up ^ [1] HM Treasury FOI response relating to a period 2008–2009. hm-treasury.gov.uk(PDF)
Jump up ^ Josie Ensor (1 April 2012). "Three pound coins in every 100 are fake". London: The Telegraph.
^ Jump up to: a b Rosie Murray-West and Harry Wallop (27 July 2010). "Record number of fake £1 coins could force reissue". London: The Telegraph.
Jump up ^ Chris Irvine (29 January 2009). "One £1 coin in 40 is a fake". London: The Telegraph.
^ Jump up to: a b Ben Ando (8 April 2009). "Fake £1 coin estimate 'doubled'". BBC News.
^ Jump up to: a b c d Fake Britain, Series 2 episode 1, first broadcast on BBC1 TV on 16 May 2011
^ Jump up to: a b c Hilary Osborne (2 April 2012) How to spot a fake £1 coin Guardian. Retrieved 24 January 2016
Jump up ^ Sarah Preece (28 July 2010). "£1 coin under threat". London: Live Odds and Scores.
Jump up ^ [2][3][4] Three blog entries analyzing counterfeits the author has been passed. blog.alism.com
^ Jump up to: a b The types of counterfeit one-pound coins and identifying them. coinauthentication.co.uk. February 2006. Retrieved 24 January 2016.
Jump up ^ "Report on UK £1 counterfeit survey" (PDF). Royal Mint. May 2009.
Jump up ^ Royal Mint Presses Last Batch of Round Pound Coins The Guardian
Jump up ^ Svenja O'Donnell (18 March 2014). "U.K. to Replace 1-Pound Coin With Secure 12-Edged Design". Bloomberg.
Jump up ^ Can I use coinage from the Channel Islands or the Isle of Man?, Royal Mint. Retrieved 24 January 2016
Jump up ^ Can I use coinage from United Kingdom Overseas Territories?, Royal Mint. Retrieved 24 January 2016
Jump up ^ "Letter From London: Real Britannia". The New Yorker (paid registration required for the full article).
Coincraft's Standard Catalogue English & UK Coins 1066 to Date, Richard Lobel, Coincraft. ISBN 0-9526228-8-2
External links[edit]
Royal Mint – £1 coin
Royal Mint - the new pound coin
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Twin prime
From Wikipedia, the free encyclopedia
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A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair.
Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger. However, it is unknown if there are infinitely many twin primes or if there is a largest pair. The work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present it remains unsolved.[1]
Unsolved problem in mathematics:
Are there infinitely many twin primes?
(more unsolved problems in mathematics)
Contents
1 History
2 Properties
2.1 Brun's theorem
3 Other theorems weaker than the twin prime conjecture
4 Conjectures
4.1 First Hardy–Littlewood conjecture
4.2 Polignac's conjecture
5 Large twin primes
6 Other elementary properties
7 Isolated prime
8 See also
9 References
10 Further reading
11 External links
History[edit]
The question of whether there exist infinitely many twin primes has been one of the great open questions in number theory for many years. This is the content of the twin prime conjecture, which states that there are infinitely many primes p such that p + 2 is also prime. In 1849, de Polignac made the more general conjecture that for every natural number k, there are infinitely many primes p such that p + 2k is also prime. The case k = 1 of de Polignac's conjecture is the twin prime conjecture.
A stronger form of the twin prime conjecture, the Hardy–Littlewood conjecture (see below), postulates a distribution law for twin primes akin to the prime number theorem.
On April 17, 2013, Yitang Zhang announced a proof that for some integer N that is less than 70 million, there are infinitely many pairs of primes that differ by N.[2] Zhang's paper was accepted by Annals of Mathematics in early May 2013.[3] Terence Tao subsequently proposed a Polymath Project collaborative effort to optimize Zhang's bound.[4] As of April 14, 2014, one year after Zhang's announcement, the bound has been reduced to 246.[5] Further, assuming the Elliott–Halberstam conjecture and its generalized form, the Polymath project wiki states that the bound has been reduced to 12 and 6, respectively.[5] These improved bounds were discovered using a different approach that was simpler than Zhang's and was discovered independently by James Maynard and Terence Tao. This second approach also gave bounds for the smallest f(m) needed to guarantee that infinitely many intervals of width f(m) contain at least m primes.
Properties[edit]
Usually the pair (2, 3) is not considered to be a pair of twin primes.[6] Since 2 is the only even prime, this pair is the only pair of prime numbers that differ by one; thus twin primes are as closely spaced as possible for any other two primes.
The first few twin prime pairs are:
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), … A077800.
Five is the only prime in two distinct pairs.
Every twin prime pair except ( 3 , 5 ) {\displaystyle (3,5)} is of the form ( 6 n − 1 , 6 n + 1 ) {\displaystyle (6n-1,6n+1)} for some natural number n; that is, the number between the two primes is a multiple of 6.[7] As a result, the sum of any pair of twin primes (other than 3 and 5) is divisible by 12.
Brun's theorem[edit]
Main article: Brun's theorem
In 1915, Viggo Brun showed that the sum of reciprocals of the twin primes was convergent.[8] This famous result, called Brun's theorem, was the first use of the Brun sieve and helped initiate the development of modern sieve theory. The modern version of Brun's argument can be used to show that the number of twin primes less than N does not exceed
C N ( log  N ) 2 {\displaystyle {\frac {CN}{(\log N)^{2}}}}
for some absolute constant C > 0.[9] In fact, it is bounded above by : C ′ N ( log  N ) 2 ( 1 + O ( log  log  N log  N ) ) {\displaystyle {\frac {C'N}{(\log N)^{2}}}\left(1+O\left({\frac {\log \log N}{\log N}}\right)\right)} , where C ′ = 8 C 2 {\displaystyle C'=8C_{2}} , where C2 is the twin prime constant, given below.[10]
Other theorems weaker than the twin prime conjecture[edit]
In 1940, Paul Erdős showed that there is a constant c < 1 and infinitely many primes p such that (p′ − p) < (c ln p) where p′ denotes the next prime after p. This result was successively improved; in 1986 Helmut Maier showed that a constant c < 0.25 can be used. In 2004 Daniel Goldston and Cem Yıldırım showed that the constant could be improved further to c = 0.085786… In 2005, Goldston, János Pintz and Yıldırım established that c can be chosen to be arbitrarily small,[11][12] i.e.
lim inf n → ∞ p n + 1 − p n log  p n = 0. {\displaystyle \liminf _{n\to \infty }{\frac {p_{n+1}-p_{n}}{\log p_{n}}}=0.}
By assuming the Elliott–Halberstam conjecture or a slightly weaker version, they were able to show that there are infinitely many n such that at least two of n, n + 2, n + 6, n + 8, n + 12, n + 18, or n + 20 are prime. Under a stronger hypothesis they showed that for infinitely many n, at least two of n, n + 2, n + 4, and n + 6 are prime.
The result of Yitang Zhang,
lim inf n → ∞ ( p n + 1 − p n ) < N with N = 7 × 10 7 , {\displaystyle \liminf _{n\to \infty }(p_{n+1}-p_{n})<N\;{\text{ with }}\;N=7\times 10^{7},}
is a major improvement on the Goldston–Graham–Pintz–Yıldırım result. The Polymath Project optimization of Zhang's bound and the work of Maynard has reduced the bound to N = 246.[13][14]
Conjectures[edit]
First Hardy–Littlewood conjecture[edit]
The Hardy–Littlewood conjecture (named after G. H. Hardy and John Littlewood) is a generalization of the twin prime conjecture. It is concerned with the distribution of prime constellations, including twin primes, in analogy to the prime number theorem. Let π2(x) denote the number of primes p ≤ x such that p + 2 is also prime. Define the twin prime constant C2 as[15]
C 2 = ∏ p p r i m e p ≥ 3 ( 1 − 1 ( p − 1 ) 2 ) ≈ 0.660161815846869573927812110014 … {\displaystyle C_{2}=\prod _{\textstyle {p\;{\rm {prime}} \atop p\geq 3}}\left(1-{\frac {1}{(p-1)^{2}}}\right)\approx 0.660161815846869573927812110014\dots }
A005597 (here the product extends over all prime numbers p ≥ 3). Then the conjecture is that
π 2 ( x ) ∼ 2 C 2 x ( ln  x ) 2 ∼ 2 C 2 ∫ 2 x d t ( ln  t ) 2 {\displaystyle \pi _{2}(x)\sim 2C_{2}{\frac {x}{(\ln x)^{2}}}\sim 2C_{2}\int _{2}^{x}{dt \over (\ln t)^{2}}}
in the sense that the quotient of the two expressions tends to 1 as x approaches infinity.[16] (The second ~ is not part of the conjecture and is proven by integration by parts.)
The conjecture can be justified (but not proven) by assuming that 1 / ln t describes the density function of the prime distribution, an assumption suggested by the prime number theorem and would imply the twin prime conjecture, but remains unresolved.
This first Hardy–Littlewood conjecture on prime k-tuples implies that the second Hardy–Littlewood conjecture is false.
Polignac's conjecture[edit]
Polignac's conjecture from 1849 states that for every positive even natural number k, there are infinitely many consecutive prime pairs p and p′ such that p′ − p = k (i.e. there are infinitely many prime gaps of size k). The case k = 2 is the twin prime conjecture. The conjecture has not yet been proven or disproven for any specific value of k, but Zhang's result proves that it is true for at least one (currently unknown) value of k. Indeed, if such a k did not exist, then for any positive even natural number N there are at most finitely many n such that pn+1 − pn = m for all m < N and so for n large enough we have pn+1 − pn > N, which would contradict Zhang's result.
Large twin primes[edit]
Beginning in 2007, two distributed computing projects, Twin Prime Search and PrimeGrid, have produced several record-largest twin primes. As of September 2018[update], the current largest twin prime pair known is 2996863034895 · 21290000 ± 1,[17] with 388,342 decimal digits. It was discovered in September 2016.[18]
There are 808,675,888,577,436 twin prime pairs below 1018.[19]
An empirical analysis of all prime pairs up to 4.35 · 1015 shows that if the number of such pairs less than x is f(x)·x/(log x)2 then f(x) is about 1.7 for small x and decreases towards about 1.3 as x tends to infinity. The limiting value of f(x) is conjectured to equal twice the twin prime constant ( A114907) (not to be confused with Brun's constant), according to the Hardy–Littlewood conjecture.
Other elementary properties[edit]
Every third odd number is divisible by 3, which requires that no three successive odd numbers can be prime unless one of them is 3. Five is therefore the only prime that is part of two twin prime pairs. The lower member of a pair is by definition a Chen prime.
It has been proven that the pair (m, m + 2) is a twin prime if and only if
4 ( ( m − 1 ) ! + 1 ) ≡ − m ( mod m ( m + 2 ) ) . {\displaystyle 4((m-1)!+1)\equiv -m{\pmod {m(m+2)}}.}
If m − 4 or m + 6 is also prime then the three primes are called a prime triplet.
For a twin prime pair of the form (6n − 1, 6n + 1) for some natural number n > 1, n must have units digit 0, 2, 3, 5, 7, or 8 ( A002822).
Isolated prime[edit]
An isolated prime (also known as single prime or non-twin prime) is a prime number p such that neither p − 2 nor p + 2 is prime. In other words, p is not part of a twin prime pair. For example, 23 is an isolated prime, since 21 and 25 are both composite.
The first few isolated primes are
2, 23, 37, 47, 53, 67, 79, 83, 89, 97, ... A007510
It follows from Brun's theorem that almost all primes are members of this sequence.
See also[edit]
Cousin prime
Prime gap
Prime k-tuple
Prime quadruplet
Prime triplet
Sexy prime
References[edit]
Jump up ^ Terry Tao, Small and Large Gaps Between the Primes
Jump up ^ McKee, Maggie (14 May 2013). "First proof that infinitely many prime numbers come in pairs". Nature. doi:10.1038/nature.2013.12989. ISSN 0028-0836.
Jump up ^ Zhang, Yitang (2014). "Bounded gaps between primes". Annals of Mathematics. 179 (3): 1121–1174. doi:10.4007/annals.2014.179.3.7. MR 3171761.
Jump up ^ Tao, Terence (June 4, 2013). "Polymath proposal: bounded gaps between primes".
^ Jump up to: a b "Bounded gaps between primes". Polymath. Retrieved 2014-03-27.
Jump up ^ The First 100,000 Twin Primes
Jump up ^ Caldwell, Chris K. "Are all primes (past 2 and 3) of the forms 6n+1 and 6n-1?". The Prime Pages. The University of Tennessee at Martin. Retrieved 2018-09-27.
Jump up ^ Brun, V. (1915), "Über das Goldbachsche Gesetz und die Anzahl der Primzahlpaare", Archiv for Mathematik og Naturvidenskab (in German), 34 (8): 3–19, ISSN 0365-4524, JFM 45.0330.16
Jump up ^ Bateman & Diamond (2004) p. 313
Jump up ^ Heini Halberstam, and Hans-Egon Richert, Sieve Methods, p. 117, Dover Publications, 2010
Jump up ^ Goldston, Daniel Alan; Motohashi, Yoichi; Pintz, János; Yıldırım, Cem Yalçın (2006), "Small gaps between primes exist", Japan Academy. Proceedings. Series A. Mathematical Sciences, 82 (4): 61–65, arXiv:math.NT/0505300, doi:10.3792/pjaa.82.61, MR 2222213 .
Jump up ^ Goldston, D. A.; Graham, S. W.; Pintz, J.; Yıldırım, C. Y. (2009), "Small gaps between primes or almost primes", Transactions of the American Mathematical Society, 361 (10): 5285–5330, arXiv:math.NT/0506067, doi:10.1090/S0002-9947-09-04788-6, MR 2515812
Jump up ^ Maynard, James (2015), "Small gaps between primes", Annals of Mathematics, Second Series, 181 (1): 383–413, arXiv:1311.4600, doi:10.4007/annals.2015.181.1.7, MR 3272929
Jump up ^ Polymath, D. H. J. (2014), "Variants of the Selberg sieve, and bounded intervals containing many primes", Research in the Mathematical Sciences, 1: Art. 12, 83, arXiv:1407.4897, doi:10.1186/s40687-014-0012-7, MR 3373710
Jump up ^ Sloane, N.J.A. (ed.). "Sequence A001692 (Number of irreducible polynomials of degree n over GF(5); dimensions of free Lie algebras)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2011-02-02. -- A page of number theoretical constants
Jump up ^ Bateman & Diamond (2004) pp.334–335
Jump up ^ Caldwell, Chris K. "The Prime Database: 2996863034895*2^1290000-1".
Jump up ^ "World Record Twin Primes Found!".
Jump up ^ Tomás Oliveira e Silva (7 April 2008). "Tables of values of pi(x) and of pi2(x)". Aveiro University. Retrieved 7 January 2011.
Bateman, Paul T.; Diamond, Harold G. (2004). Analytic Number Theory. World Scientific. ISBN 981-256-080-7. Zbl 1074.11001.
Further reading[edit]
Sloane, Neil; Plouffe, Simon (1995). The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press. ISBN 0-12-558630-2.
External links[edit]
Hazewinkel, Michiel, ed. (2001) [1994], "Twins", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Top-20 Twin Primes at Chris Caldwell's Prime Pages
Xavier Gourdon, Pascal Sebah: Introduction to Twin Primes and Brun's Constant
"Official press release" of 58711-digit twin prime record
Weisstein, Eric W. "Twin Primes". MathWorld.
The 20 000 first twin primes
Polymath: Bounded gaps between primes
Sudden Progress on Prime Number Problem Has Mathematicians Buzzing
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