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Chen Prime
In mathematics, 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 m ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19 (number)
19 (nineteen) is the natural number following 18 (number), 18 and preceding 20 (number), 20. It is a prime number. Mathematics Nineteen is the eighth prime number. Number theory 19 forms a twin prime with 17 (number), 17, a cousin prime with 23 (number), 23, and a sexy prime with 13 (number), 13. 19 is the fifth Trinomial triangle#Central trinomial coefficients, central trinomial coefficient, and the maximum number of fourth powers needed to sum up to any natural number (see, Waring's problem). It is the number of Composition (combinatorics), compositions of 8 into distinct parts. 19 is the eighth strictly non-palindromic number in any Numeral system, base, following 11 (number), 11 and preceding 47 (number), 47. 19 is also the second octahedral number, after 6, and the sixth Heegner number. In the Engel expansion of pi, 19 is the seventh term following and preceding . The sum of the first terms preceding 17 (number), 17 is in equivalence with 19, where its prime Sequen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
101 (number)
101 (one hundred ndone) is the umberfollowing 100 and preceding 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, 101st (one hundred ndfirst), rather than 101th, is the correct form. 101 is a prime number and the smallest integer above 100. It is also a palindromic number, and hence, a palindromic prime. In mathematics 101 is an alternating factorial, sexy prime and 101 is also the smallest number that can be expressed as the sum of three distinct nonzero squares in more than two ways: 9^2+4^2+2^2, 8^2+6^2+1^2 or 7^2+6^2+4^2 (see image). For a 3-digit number in decimal, this number has a relatively simple divisibility test. The candidate number is split into groups of four, starting with the rightmost four, and added up to produce a 4-digit number. If this 4-digit number is of the form 1000a+100b+10a+b (where and are integers from 0 to 9), such as 3232 or 9797 ... [...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 . * The 11th 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. ... [...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. * the number of primes that are right-truncatable. * a super-prime, because 23 is prime. In other fields * The eighth letter of the alphabet is H and the third letter is C, thus 83 stands for "Heil Christ," a greeting used by organizations that consider themselves also to be Christian. * An emoticon An emoticon (, , rarely , ), short for emotion icon, is a pictorial representation of a facial expression using Character (symbol), characters—usually punctuation marks, numbers and Alphabet, l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
71 (number)
71 (seventy-one) is the natural number following 70 and preceding 72. __TOC__ In mathematics 71 is the 20th prime number. Because both rearrangements of its digits (17 and 71) are prime numbers, 71 is an emirp and more generally a permutable prime. 71 is a centered heptagonal number. It is a regular prime, a Ramanujan prime, a Higgs prime, and a good prime. It is a Pillai prime, since 9!+1 is divisible by 71, but 71 is not one more than a multiple of 9. It is part of the last known pair (71, 7) of Brown numbers, since 71^=7!+1. 71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also, Heegner number In number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from int ...s). 71 is the largest number which occurs as a prim ... [...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 and prime 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 Twin prime#Isolated prime, isolated prime. (65 and 69 are not prime) *a sexy prime with 61 and 73 References External links Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
59 (number)
59 (fifty-nine) is the natural number following 58 (number), 58 and preceding 60 (number), 60. In mathematics Fifty-nine is the 17th prime number, and 7th super-prime. It is also a good prime, a Higgs prime, an Regular prime#Irregular primes, irregular prime, a Pillai prime, a Ramanujan prime, a Safe and Sophie Germain primes, safe prime, and a Supersingular prime (moonshine theory), supersingular prime, The next prime number is sixty-one, with which it comprises a twin prime. There are 59 stellations of the regular icosahedron. In other fields Fifty-nine is: * The number corresponding to the last minute in a given hour, and the last second in a given minute ** The "59-minute rule" is an informal rule in business, whereby (usually near a holiday) employees may be allowed to leave work early, often to beat heavy holiday traffic (the 59 minutes coming from the rule that leaving one full hour early requires the use of leave, whereas leaving 59 minutes early would not) * The number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
53 (number)
53 (fifty-three) is the natural number following 52 (number), 52 and preceding 54 (number), 54. It is the 16th prime number. In mathematics Fifty-three is the 16th prime number. It is the second balanced prime, and fifth isolated prime. 53 is a sexy prime with 47 (number), 47 and 59 (number), 59. It is the eighth Sophie Germain prime, and the ninth Eisenstein prime. The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by only a few other numbers. 53 cannot be expressed as the sum of any integer and its decimal digits, making 53 the ninth self number in decimal. 53 is the smallest prime number that does not divide the order of any sporadic group, inclusive of the six Pariah group, pariahs; it is also the first prime number that is not a member of Bhargava's prime-universality criterion theorem (followed by the next prime number 59 (number), 59), an integer-matrix quadratic form that represents all prime numbers when it represents the sequence of s ... [...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. It is the adopted favorite number of Pomona College, a liberal arts college in Southern California, whose alumni have added cultural references to it in numerous places, including many ''Star Trek'' episodes. Mathematics 47 is a safe prime, a Thabit number, Thabit prime, a regular prime, a cluster prime, an isolated prime, a Ramanujan prime, and a Higgs prime. 47 is also a supersingular prime (moonshine theory), supersingular prime. It is the last consecutive prime number that divides the order of at least one sporadic group. In popular culture Pomona College Other Late rapper Capital Steez was infatuated with the number 47 and what it meant spiritually. He believed the number 47 was the "perfect expression of balance in the world", representing the tension between the heart and the brain (the fourth and seventh chakras, respectively.) The number featured on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
41 (number)
41 (forty-one) is the natural number following 40 (number), 40 and preceding 42 (number), 42. In mathematics 41 is: * the 13th smallest prime number. The next is 43 (number), 43, making both twin primes. * the sum of the first six prime numbers (2 + 3 + 5 + 7 + 11 + 13). * a regular prime * a Ramanujan prime * a harmonic prime * a good prime * the 12th Supersingular prime (moonshine theory), supersingular prime * a Newman–Shanks–Williams prime. * the smallest Sophie Germain prime to start a Cunningham chain of the first kind of three terms, . * an Eisenstein prime, with no imaginary part and real part of the form 3''n'' − 1. * a Proth prime as it is 5 × 23 + 1. * the smallest Lucky numbers of Euler, lucky number of Euler: the polynomial yields primes for all the integers ''k'' with . * the sum of two Square number, squares (42 + 52), which makes it a centered square number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
37 (number)
37 (thirty-seven) is the natural number following 36 and preceding 38. In mathematics 37 is the 12th prime number, and the 3rd isolated prime without a twin prime. 37 is the first irregular prime with irregularity index of 1, where the smallest prime number with an irregularity index of 2 is the thirty-seventh prime number, 157. The smallest magic square, using only primes and 1, contains 37 as the value of its central cell: Its magic constant is 37 x 3 = 111, where 3 and 37 are the first and third base-ten unique primes (the second such prime is 11). 37 requires twenty-one steps to return to 1 in the Collatz problem, as do adjacent numbers 36 and 38. The two closest numbers to cycle through the elementary Collatz pathway are 5 and 32, whose sum is 37; also, the trajectories for 3 and 21 both require seven steps to reach 1. On the other hand, the first two integers that return 0 for the Mertens function ( 2 and 39) have a difference of 37, where the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
