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This is a list of articles about prime numbers.A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers.
The first five of these numbers – 3, 5, 17, 257, and 65,537 – are prime, [172] but is composite and so are all other Fermat numbers that have been verified as of 2017. [173] A regular n {\displaystyle n} -gon is constructible using straightedge and compass if and only if the odd prime factors of n {\displaystyle n} (if any ...
863282×5 5179692 - 1 17 October 2024 3,620,456 105 670490×12 3352450 - 1 17 October 2024 3,617,907 106 4×3 7578378 + 1 9 September 2024 3,615,806 107 11×2 11993994 − 1 15 August 2024 3,610,554 108 3761×2 11978874 − 1 6 July 2022 3,606,004 109 95×2 11954552 − 1 28 May 2024 3,598,681 110 259072×5 5136295 − 1 28 October 2024 ...
For example, the AP-3 {3, 7, 11} does not qualify, because 5 is also a prime. For an integer k ≥ 3, a CPAP-k is k consecutive primes in arithmetic progression. It is conjectured there are arbitrarily long CPAP's. This would imply infinitely many CPAP-k for all k. The middle prime in a CPAP-3 is called a balanced 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.
All permutable primes of two or more digits are composed from the digits 1, 3, 7, 9, because no prime number except 2 is even, and no prime number besides 5 is divisible by 5. It is proven [ 4 ] that no permutable prime exists which contains three different of the four digits 1, 3, 7, 9, as well as that there exists no permutable prime composed ...
For example, to find the seventh Fortunate number, one would first calculate the product of the first seven primes (2, 3, 5, 7, 11, 13 and 17), which is 510510. Adding 2 to that gives another even number, while adding 3 would give another multiple of 3. One would similarly rule out the integers up to 18.
41, 83, 167 (The next number would be 335, but that is not prime.) 89, 179, 359, 719, 1439, 2879 (The next number would be 5759, but that is not prime.) Examples of complete Cunningham chains of the second kind include these: 2, 3, 5 (The next number would be 9, but that is not prime.) 7, 13 (The next number would be 25, but that is not prime.)