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Chen Prime
A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingrun, who proved in 1966 that there are infinitely many such primes. This result would also follow from the truth of the twin prime conjecture as the lower member of a pair of twin primes is by definition a Chen prime. The first few Chen primes are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, … . The first few Chen primes that are not the lower member of a pair of twin primes are :2, 7, 13, 19, 23, 31, 37, 47, 53, 67, 83, 89, 109, 113, 127, ... . The first few non-Chen primes are :43, 61, 73, 79, 97, 103, 151, 163, 173, 193, 223, 229, 241, … . All of the supersingular primes are Chen primes. Rudolf Ondrejka discovered the following 3 × 3 magic square of n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chen Jingrun
Chen Jingrun (; 22 May 1933 – 19 March 1996), also known as Jing-Run Chen, was a Chinese mathematician who made significant contributions to number theory, including Chen's theorem and the Chen prime. Life and career Chen was the third son in a large family from Fuzhou, Fujian, China. His father was a postal worker. Chen Jingrun graduated from the Mathematics Department of Xiamen University in 1953. His advisor at the Chinese Academy of Sciences was Hua Luogeng. His work on the twin prime conjecture, Waring's problem, Goldbach's conjecture and Legendre's conjecture led to progress in analytic number theory. In a 1966 paper he proved what is now called Chen's theorem: every sufficiently large even number can be written as the sum of a prime and a semiprime (the product of two primes) – e.g., 100 = 23 + 7·11. Despite being persecuted during the Cultural Revolution, he expanded his proof in the 1970s. After the end of the Cultural Revolution, Xu Chi wro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
29 (number)
29 (twenty-nine) is the natural number following 28 and preceding 30. Mathematics * 29 is the tenth prime number, and the fourth primorial prime. * 29 forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. * 29 is the sum of three consecutive squares, 22 + 32 + 42. * 29 is a Lucas prime, a Pell prime, and a tetranacci number. * 29 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 the first 29 natural numbers have more than two different prime factors. This is the longest such consecutive sequence. * 29 is a Markov number, appearing in the solutions to ''x'' + ''y'' + ''z'' = 3''xyz'': , , , , etc. * 29 is a Perrin number, preceded in the sequence by 12, 17, 22. * 29 is the smallest positive whole number that cannot be made from the numbers , using each exactly once and using only addition, subtraction, multiplication, and div ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersingular Prime (moonshine Theory)
In the mathematical branch of moonshine theory, a supersingular prime is a prime number that divides the order of the Monster group ''M'', which is the largest sporadic simple group. There are precisely fifteen supersingular prime numbers: the first eleven primes ( 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31), as well as 41, 47, 59, and 71. The non-supersingular primes are 37, 43, 53, 61, 67, and any prime number greater than or equal to 73. Supersingular primes are related to the notion of supersingular elliptic curves as follows. For a prime number ''p'', the following are equivalent: # The modular curve ''X''0+(''p'') = ''X''0(''p'') / ''w''p, where ''w''p is the Fricke involution of ''X''0(''p''), has genus zero. # Every supersingular elliptic curve in characteristic ''p'' can be defined over the prime subfield F''p''. # The order of the Monster group is divisible by ''p''. The equivalence is due to Andrew Ogg. More precisely, in 1975 Ogg showed that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
101 (number)
101 (one hundred [and] one) is the natural number following 100 (number), 100 and preceding 102 (number), 102. It is variously pronounced "one hundred and one" / "a hundred and one", "one hundred one" / "a hundred one", and "one oh one". As an Ordinal number (linguistics), ordinal number, 101st (one hundred [and] first), rather than 101th, is the correct form. In mathematics 101 is: *the 26th prime number, and the smallest above 100. *a palindromic number in base 10, and so a palindromic prime. *a Chen prime since 103 (number), 103 is also prime, with which it makes a twin prime pair. *a sexy prime since 107 and 113 are also prime, with which it makes a sexy prime triplet. *a unique prime, because the period length of its reciprocal is unique among primes. *an Eisenstein prime with no imaginary part and real part of the form 3n - 1. *the fifth alternating factorial. *a centered decagonal number. *the only existing prime with alternating 1s and 0s in base 10 and the largest known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
89 (number)
89 (eighty-nine) is the natural number following 88 and preceding 90. In mathematics 89 is: * the 24th prime number, following 83 and preceding 97. * a Chen prime. * a Pythagorean prime. * the smallest Sophie Germain prime to start a Cunningham chain of the first kind of six terms, . * an Eisenstein prime with no imaginary part and real part of the form . * a Fibonacci number and thus a Fibonacci prime as well. The first few digits of its reciprocal coincide with the Fibonacci sequence due to the identity ::\frac=\sum_^\infty=0.011235955\dots\ . * a Markov number, appearing in solutions to the Markov Diophantine equation with other odd-indexed Fibonacci numbers. ''M''89 is the 10th Mersenne prime. Although 89 is not a Lychrel number in base 10, it is unusual that it takes 24 iterations of the reverse and add process to reach a palindrome. Among the known non-Lychrel numbers in the first 10000 integers, no other number requires that many or more iterations. The palindrome r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
83 (number)
83 (eighty-three) is the natural number following 82 and preceding 84. In mathematics 83 is: * the sum of three consecutive primes (23 + 29 + 31). * the sum of five consecutive primes (11 + 13 + 17 + 19 + 23). * the 23rd prime number, following 79 (of which it is also a cousin prime) and preceding 89. * a Sophie Germain prime. * a safe prime. * a Chen prime. * an Eisenstein prime with no imaginary part and real part of the form 3''n'' − 1. * a highly cototient number. * there number of primes that are right-truncatable. * a super-prime, because 23 is prime. In science Chemistry *The atomic number of bismuth (Bi) Astronomy * Messier object M83, a magnitude 8.5 spiral galaxy in the constellation Hydra, also known as the Southern Pinwheel Galaxy *The New General Catalogue object NGC 83, a magnitude 12.3 elliptical galaxy in the constellation Andromeda In religion Judaism * When someone reaches 83 they may celebrate a second bar mitzvah In music * M83 is the debut a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
71 (number)
71 (seventy-one) is the natural number following 70 (number), 70 and preceding 72 (number), 72. __TOC__ In mathematics 71 is: *the 20th prime number. The next is 73 (number), 73, with which it composes a twin prime. *a permutable prime and emirp with 17 (number), 17. *is the largest number which occurs as a prime factor of an order of a sporadic simple group. *the sum of three consecutive primes: 19 (number), 19, 23 (number), 23 and 29 (number), 29. *a centered heptagonal number. *an Eisenstein prime with no imaginary part and real part of the form 3''n'' – 1. *a Pillai prime, since 9! + 1 is divisible by 71 but 71 is not one more than a multiple of 9. *the largest (15th) Supersingular prime (moonshine theory), supersingular prime, which is also a Chen prime. *part of the last known pair (71, 7) of Brown numbers, since 712 = 7! + 1. *the twenty-third term of the Euclid–Mullin sequence, as it is the least prime factor of one more than th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
67 (number)
67 (sixty-seven) is the natural number following 66 (number), 66 and preceding 68 (number), 68. It is an Parity (mathematics), odd number. In mathematics 67 is: *the 19th prime number (the next is 71 (number), 71). * a Chen prime. *an irregular prime. *a lucky prime. *the sum of five consecutive primes (7 + 11 + 13 + 17 + 19). *a Heegner number. *a Pillai prime since 18! + 1 is divisible by 67, but 67 is not one more than a multiple of 18. *palindromic in quinary (2325) and senary (1516). *a super-prime. (19 is prime) *an isolated prime. (65 and 69 aren't prime) In science *The atomic number of holmium, a lanthanide. Astronomy *Messier object Messier 67, M67, a visual magnitude, magnitude 7.5 open cluster in the constellation Cancer (constellation), Cancer. *The New General Catalogue object NGC 67, an elliptical galaxy in the constellation Andromeda (constellation), Andromeda. In music * "Car 67", a song by the band Driver 67 * Chicago (band), Chicago's song "Questions 67 and 6 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
59 (number)
59 (fifty-nine) is the natural number following 58 and preceding 60. In mathematics Fifty-nine is the 17th prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary part and real part of the form . Since is divisible by 59 but 59 is not one more than a multiple of 15, 59 is a Pillai prime. It is also a highly cototient number. There are 59 stellations of the regular icosahedron, inclusive of the icosahedron. 59 is one of the factors that divides the smallest composite Euclid number. In this case 59 divides the Euclid number 13 # + 1 = 2 × 3 × 5 × 7 × 11 × 13 + 1 = 59 × 509 = 30031. 59 is the highest integer a single symbol may represent in the Sexagesimal system. As 17 is prime, 59 is a super-prime. The number 59 takes 3 iterations of the "reverse and add" process to form the palindrome 1111. All smaller integers (1 through 58) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
53 (number)
53 (fifty-three) is the natural number following 52 and preceding 54. It is the 16th prime number. In mathematics *Fifty-three is the 16th prime number. It is also an Eisenstein prime, an isolated prime, a balanced prime and a Sophie Germain prime. *The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by only a few other numbers. *In hexadecimal, 53 is 35, that is, the same characters used in the decimal representation, but reversed. Four additional multiples of 53 share this property: 371 = , 5141 = , 99,481 = , and 8,520,280 = 0. Apart from the trivial case of single-digit decimals, no other number has this property. *53 cannot be expressed as the sum of any integer and its decimal digits, making 53 a self number. *53 is the smallest prime number that does not divide the order of any sporadic group. In science *The atomic number of iodine Astronomy *Messier object M53, a magnitude 8.5 globular cluster in the constellation Coma Berenices *The N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
47 (number)
47 (forty-seven) is the natural number following 46 (number), 46 and preceding 48 (number), 48. It is a prime number. In mathematics Forty-seven is the fifteenth prime number, a safe prime, the thirteenth supersingular prime (moonshine theory), supersingular prime, the fourth isolated prime, and the sixth Lucas prime. Forty-seven is a highly cototient number. It is an Eisenstein prime with no imaginary part and real part of the form . It is a Lucas number. It is also a Keith number because its digits appear as successive terms earlier in the series of Lucas numbers: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... It is the number of Tree (graph theory), trees on 9 unlabeled nodes. Forty-seven is a strictly non-palindromic number. Its representation in binary being 101111, 47 is a prime Thabit number, and as such is related to the pair of amicable numbers . In science * 47 is the atomic number of silver. Astronomy * The 47-year cycle of Mars: after 47 years – 22 Synodic period, synodic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
