Which is the only prime number between 90 and 100?
"the first nine prime numbers, as well as the sum of some pairs of prime numbers e.g., 3 + 97, 11 + 89, 17 + 83, 29 + 71, 41 + 59, and 47 + 53. 100 is the sum of the cubes of the first four integers (100 = 1 + 2 + 3 + 4). This is related by Nicomachus's theorem to the fact that 100 also equals the square of the sum of the first four integers: . 2 + 6 = 100, thus 100 is a Leyland number. 100 is an 18-gonal number. It is divisible"
"90 (number) 90 (ninety) is the natural number preceded by 89 and followed by 91. In the English language, the numbers 90 and 19 are often confused, as sounding very similar. When carefully enunciated, they differ in which syllable is stressed: 19 /naɪnˈtiːn/ vs 90 /ˈnaɪnti/. However, in dates such as 1999, and when contrasting numbers in the teens and when counting, such as 17, 18, 19, the stress shifts to the first syllable: 19 /ˈnaɪntiːn/. 90 is: In normal space, the interior angles of a rectangle measure 90 degrees each. Also, in a right triangle, the angle opposing the"
"Unique prime In recreational number theory, a unique prime or unique period prime is a certain kind of prime number. A prime ""p"" ≠ 2, 5 is called unique if there is no other prime ""q"" such that the period length of the decimal expansion of its reciprocal, 1 / ""p"", is equal to the period length of the reciprocal of ""q"", 1 / ""q"". For example, 3 is the only prime with period 1, 11 is the only prime with period 2, 37 is the only prime with period 3, 101 is the only prime with period 4, so"
"is the only triplet that can ever be prime. 111 is not prime in base ten, but is prime in base two, where 111 = 7. It is also prime in these other bases up to 128: 3, 5, 6, 8, 12, 14, 15, 17, 20, 21, 24, 27, 33, 38, 41, 50, 54, 57, 59, 62, 66, 69, 71, 75, 77, 78, 80, 89, 90, 99, 101, 105, 110, 111, 117, 119 In base 18, the number 111 is 7 (= 343) which is the only base where 111 is a perfect power. The smallest magic square using only"
"Prime gap A prime gap is the difference between two successive prime numbers. The ""n""-th prime gap, denoted ""g"" or ""g""(""p"") is the difference between the (""n"" + 1)-th and the ""n""-th prime numbers, i.e. We have ""g"" = 1, ""g"" = ""g"" = 2, and ""g"" = 4. The sequence (""g"") of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered. The first 60 prime gaps are: By the definition of ""g"" every prime can be written as The first, smallest, and only odd prime gap is the gap of size 1 between 2, the"
"additional insight into Gilbreath's conjecture on the differences of consecutive prime numbers. In the triangle of numbers generated from the primes by repeatedly applying the forward difference operator, it appears that most values are either 0 or 2. In particular, Gilbreath's conjecture asserts that the leftmost values in each row of this triangle are all 0 or 2. When a contiguous subsequence of values in one row of the triangle are all 0 or 2, then Rule 90 can be used to determine the corresponding subsequence in the next row. explained the rule by a metaphor of tree growth in"
"""proven"" unique prime was (10 + 1)/10001 or, using the notation above, (99990000)+ 1. It has 1128 digits. The record has been improved many times since then. the largest proven unique prime is formula_45, it has 20160 digits. The first unique primes in binary (base 2) are: The period length of them are: They include Fermat primes (the period length is a power of 2), Mersenne primes (the period length is a prime) and Wagstaff primes (the period length is twice an odd prime). Additionally, if ""n"" is a natural number which is not equal to 1 or 6, than"
"120 (number) 120, read as one hundred [and] twenty, is the natural number following 119 and preceding 121. In the Germanic languages, the number 120 was also formerly known as ""one hundred"". This ""hundred"" of six score is now obsolete, but is described as the long hundred or great hundred in historical contexts. 120 is the factorial of 5 and one less than a square, making (5, 11) a Brown number pair. 120 is the sum of a twin prime pair (59 + 61) and the sum of four consecutive prime numbers (23 + 29 + 31 + 37), four"
"the prime numbers from 2 to 97 are: where ? indicates that the position (or whether it exists at all) is unknown as of 2012. A related sequence of numbers determined by the largest prime factor of one plus the product of the previous numbers (rather than the smallest prime factor) is also known as the Euclid–Mullin sequence. It grows more quickly, but is not monotonic. The numbers in this sequence are Not every prime number appears in this sequence, and the sequence of missing primes, has been proven to be infinite. It is also possible to generate modified versions"
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"3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 47, 3, 1, 5, 3, ... . proved that this sequence contains only ones and prime numbers. However, it does not contain all the prime numbers, since the terms gcd(""n""+1, ""a"") are always odd and so never equal to 2. 587 is the smallest prime not appearing in the first 10,000 outcomes that are different from 1. Nevertheless, in the same paper it was conjectured to contain all (odd) primes, even though it is rather inefficient. Note"
"hypotenuse measures 90 degrees, with the other two angles adding up to 90 for a total of 180 degrees. Thus, an angle measuring 90 degrees is called a right angle. Ninety is: 90 (number) 90 (ninety) is the natural number preceded by 89 and followed by 91. In the English language, the numbers 90 and 19 are often confused, as sounding very similar. When carefully enunciated, they differ in which syllable is stressed: 19 /naɪnˈtiːn/ vs 90 /ˈnaɪnti/. However, in dates such as 1999, and when contrasting numbers in the teens and when counting, such as 17, 18, 19, the"
"179 (number) 179 (one hundred [and] seventy-nine) is the natural number following 178 and preceding 180. 179 is an odd number. 179 is a prime number; that is, it is not divisible by integer (except for 1 and itself). It is an Eisenstein prime, as it is indivisible even by complex Gaussian integers. It is a Chen prime, being two less than another prime, 181. It is a full reptend prime, meaning 1/179 has a decimal expansion of a repeated sequence of 178 digits. 179 is a safe prime, as it is one more than two times the prime 89."
"Truncatable prime In number theory, a left-truncatable prime is a prime number which, in a given base, contains no 0, and if the leading (""left"") digit is successively removed, then all resulting numbers are prime. For example, 9137, since 9137, 137, 37 and 7 are all prime. Decimal representation is often assumed and always used in this article. A right-truncatable prime is a prime which remains prime when the last (""right"") digit is successively removed. 7393 is an example of a right-truncatable prime, since 7393, 739, 73, 7 are all prime. There are 4260 left-truncatable primes and 83 right-truncatable primes."
"110 (number) 110 (""one hundred [and] ten"") is the natural number following 109 and preceding 111. 110 is a sphenic number and a pronic number. Following the prime quadruplet (101, 103, 107, 109), at 110, the Mertens function reaches a low of −5. 110 is the sum of three consecutive squares, formula_1. 110 is the side of the smallest square that can be tiled with distinct integer-sided squares. RSA-110 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. The Rule 110 cellular automaton, like Conway's Game of Life, exhibits what Stephen Wolfram calls"
"an Eisenstein prime with no imaginary part and real part of the form . It is also the only number that is part of more than one pair of twin primes. Five is a congruent number. Five is conjectured to be the only odd untouchable number and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree. Five is also the only prime that is the sum of two consecutive primes, namely 2 and 3. The number 5 is the fifth Fibonacci number, being plus . It"
"to determine a single digit in the result. There are no nontrivial reversible elementary cellular automata. However, a near-miss is provided by Rule 90 and other elementary cellular automata based on the exclusive or function. In Rule 90, the state of each cell is the exclusive or of the previous states of its two neighbors. This use of the exclusive or makes the transition rule locally invertible, in the sense that any contiguous subsequence of states can be generated by this rule. Rule 90 is not a reversible cellular automaton rule, because in Rule 90 every assignment of states to"
"Super-prime Super-prime numbers (also known as higher-order primes or prime-indexed primes) are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins That is, if ""p""(""i"") denotes the ""i""th prime number, the numbers in this sequence are those of the form ""p""(""p""(""i"")). used a computer-aided proof (based on calculations involving the subset sum problem) to show that every integer greater than 96 may be represented as a sum of distinct super-prime numbers. Their proof relies on a result resembling Bertrand's postulate, stating that (after the larger gap between super-primes 5 and"
"is a unique prime of period ""n"" in base 2 if and only if there exists a natural number ""c"" such that The only known values of ""n"" such that formula_53 is composite but formula_54 is prime are 18, 20, 21, 54, 147, 342, 602, and 889 (in these case, formula_53 has a small factor which divides ""n""). It is a conjecture that there is no other ""n"" with this property. All other known base 2 unique primes are of the form formula_53. In fact, no prime with ""c"" > 1 (that is formula_54 is a ""true power"" of ""p"")"
"term is used to refer only to pandigital numbers with no redundant digits. In some cases, a number might be called pandigital even if it doesn't have a zero as a significant digit, for example, 923456781 (these are sometimes referred to as ""zeroless pandigital numbers""). No base 10 pandigital number can be a prime number if it doesn't have redundant digits. The sum of the digits 0 to 9 is 45, passing the divisibility rule for both 3 and 9. The first base 10 pandigital prime is 10123457689; lists more. For different reasons, redundant digits are also required for a"
"121 (number) 121 (one hundred [and] twenty-one) is the natural number following 120 and preceding 122. One hundred [and] twenty-one is a square and is the sum of three consecutive primes (37 + 41 + 43). There are no squares besides 121 known to be of the form formula_1, where ""p"" is prime (3, in this case). Other such squares must have at least 35 digits. There are only two other squares known to be of the form n! + 1, supporting Brocard's conjecture. Another example of 121 being of the few examples supporting a conjecture is that Fermat conjectured"
"100 (number) 100 or one hundred (Roman numeral: Ⅽ) is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the short hundred or five score in order to differentiate the English and Germanic use of ""hundred"" to describe the long hundred of six score or 120. 100 is the square of 10 (in scientific notation it is written as 10). The standard SI prefix for a hundred is ""hecto-"". 100 is the basis of percentages (""per cent"" meaning ""per hundred"" in Latin), with 100% being a full amount. 100 is the sum of"
"a rule table that specifies the new value for each possible combination of neighboring values. In the case of Rule 90, each cell's new value is the exclusive or of the two neighboring values. Equivalently, the next state of this particular automaton is governed by the following rule table: The name of Rule 90 comes from Stephen Wolfram's binary-decimal notation for one-dimensional cellular automaton rules. To calculate the notation for the rule, concatenate the new states in the rule table into a single binary number, and convert the number into decimal: 01011010 = 90. Rule 90 has also been called"
"leads to a different but equivalent definition of the primes: they are the numbers with exactly two positive divisors, 1 and the number itself. Yet another way to say the same thing is that a number formula_1 is prime if it is greater than one and if none of the numbers formula_10 divides formula_1 evenly. The first 25 prime numbers (all the prime numbers less than 100) are: No even number formula_1 greater than 2 is prime because any such number can be expressed as the product formula_13. Therefore, every prime number other than 2 is an odd number, and"
"105 (number) 105 (one hundred [and] five) is the natural number following 104 and preceding 106. 105 is a triangular number, a dodecagonal number and the first Zeisel number. It is a sphenic number, and is the product of three consecutive prime numbers. 105 is the double factorial of 7. It is also the sum of the first five square pyramidal numbers. 105 comes in the middle of the prime quadruplet (101, 103, 107, 109). The only other such odd numbers less than a thousand are 9, 15, 195 and 825. 105 is also a pseudoprime to the prime bases"
"function. The function is neither multiplicative nor additive. Prime gap A prime gap is the difference between two successive prime numbers. The ""n""-th prime gap, denoted ""g"" or ""g""(""p"") is the difference between the (""n"" + 1)-th and the ""n""-th prime numbers, i.e. We have ""g"" = 1, ""g"" = ""g"" = 2, and ""g"" = 4. The sequence (""g"") of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered. The first 60 prime gaps are: By the definition of ""g"" every prime can be written as The first, smallest, and only odd prime gap is"
"Prime number A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 6 is composite because it is the product of two numbers () that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either"
"by 25, the number of primes below it. It can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient. It can be expressed as a sum of some of its divisors, making it a semiperfect number. 100 is a Harshad number in base 10, and also in base 4, and in that base it is a self-descriptive number. There are exactly 100 prime numbers whose digits are in strictly ascending order (e.g. 239, 2357 etc.). 100 is the smallest number whose common logarithm is a prime number (i.e. 10"
"biography of Paul Erdős, ""The man who loved only numbers"", the Wilf sequence is cited but with the initial terms switched. The resulting sequence appears primefree for the first hundred terms or so, but term 138 is the 45-digit prime 439351292910452432574786963588089477522344721. Several other primefree sequences are known: The sequence of this type with the smallest known initial terms has Primefree sequence In mathematics, a primefree sequence is a sequence of integers that does not contain any prime numbers. More specifically, it usually means a sequence defined by the same recurrence relation as the Fibonacci numbers, but with different initial conditions"
"19 (number) 19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number. In English speech, the numbers 19 and 90 are sometimes confused, as they sound very similar. 19 is the 8th prime number. 19 is the seventh Mersenne prime exponent. 19 is the maximum number of fourth powers needed to sum up to any natural number. It is the fourth value of g(k). 19 is the lowest prime centered triangular number, a centered hexagonal number and a Heegner number. The only non-trivial normal magic hexagon contains 19 hexagons (the other being 1). In"
"29 (number) 29 (twenty-nine) is the natural number following 28 and preceding 30. It is the tenth prime number, and also the fourth primorial prime. It forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. It is also the sum of three consecutive squares, 2 + 3 + 4. It is a Lucas prime, a Pell prime, and a tetranacci number. It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. 29 is also the 10th supersingular prime. None of"
"Rule 90 In the mathematical study of cellular automata, Rule 90 is an elementary cellular automaton based on the exclusive or function. It consists of a one-dimensional array of cells, each of which can hold either a 0 or a 1 value. In each time step all values are simultaneously replaced by the exclusive or of their two neighboring values. call it ""the simplest non-trivial cellular automaton"", and it is described extensively in Stephen Wolfram's 2002 book ""A New Kind of Science"". When started from a single live cell, Rule 90 has a time-space diagram in the form of a"
"by ""F"", so, apart from ""F"" = 3, any Fibonacci prime must have a prime index. As there are arbitrarily long runs of composite numbers, there are therefore also arbitrarily long runs of composite Fibonacci numbers. No Fibonacci number greater than ""F"" = 8 is one greater or one less than a prime number. The only nontrivial square Fibonacci number is 144. Attila Pethő proved in 2001 that there is only a finite number of perfect power Fibonacci numbers. In 2006, Y. Bugeaud, M. Mignotte, and S. Siksek proved that 8 and 144 are the only such non-trivial perfect powers."