Введение
Простое число p, где p+2 является простым или полупростым.
Prime number p where p+2 is prime or semiprime
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
В математике простое число p называется числом Чена, если p+2 является либо простым числом, либо произведением двух простых чисел (также называемым полупростым). Четное число 2p + 2, следовательно, удовлетворяет теореме Чена. Числа Чена названы в честь Чен Цзинруна, который в 1966 году доказал, что таких чисел бесконечно много. Этот результат также следует из истинности гипотезы о простых числах-близнецах, поскольку меньший член пары простых чисел-близнецов по определению является числом Чена. Первые несколько чисел Чена:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101.
Prime number p where p+2 is prime or semiprime
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
Первые несколько чисел Чена, которые не являются меньшим членом пары простых чисел-близнецов:
Prime number p where p+2 is prime or semiprime
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
2, 7, 13, 19, 23, 31, 37, 47, 53, 67, 83, 89, 109, 113, 127.
Prime number p where p+2 is prime or semiprime
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
Первые несколько чисел, не являющихся числами Чена:
Prime number p where p+2 is prime or semiprime
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
43, 61, 73, 79, 97, 103, 151, 163, 173, 193, 223, 229, 241.
Prime number p where p+2 is prime or semiprime
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
Все суперсингулярные простые числа являются числами Чена. Рудольф Ондрейка обнаружил следующий магический квадрат 3×3, состоящий из девяти чисел Чена:
17 89 71 113 59 5 47 29 101.
Prime number p where p+2 is prime or semiprime
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
По состоянию на 2018 год, наибольшее известное число Чена равно 2996863034895 × 21290000 − 1, и содержит 388342 десятичных цифр. Сумма обратных величин чисел Чена сходится.
Prime number p where p+2 is prime or semiprime
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
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 2p + 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 nine Chen primes:
17 89 71 113 59 5 47 29 101
as of 2018, the largest known Chen prime is 2996863034895 × 21290000 − 1, with 388342 decimal digits. The sum of the reciprocals of Chen primes converges.
Дальнейшие результаты
Чен также доказал следующее обобщение: для любого четного целого числа h существует бесконечно много простых чисел p, таких что p + h является либо простым, либо полупростым. Бен Грин и Теренс Тао показали, что числа Чена содержат бесконечно много арифметических прогрессий длиной 3. Бинбин Чжоу обобщил этот результат, показав, что числа Чена содержат арифметические прогрессии произвольной длины.
Chen also proved the following generalization: For any even integer h, there exist infinitely many primes p such that p + h is either a prime or a semiprime. Ben Green and Terence Tao showed that the Chen primes contain infinitely many arithmetic progressions of length 3. Binbin Zhou generalized this result by showing that the Chen primes contain arbitrarily long arithmetic progressions.