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a lucky prime. [3] the sum of five consecutive primes (7 + 11 + 13 + 17 + 19). a Heegner number. [4] a Pillai prime since 18! + 1 is divisible by 67, but 67 is not one more than a multiple of 18. [5] palindromic in quinary (232 5) and senary (151 6). a super-prime. (19 is prime) an isolated prime. (65 and 69 are not prime) a sexy prime with 61 ...
A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 ... 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227 ...
The existence of arbitrarily large prime gaps can be seen by noting that the sequence ! +,! +, …,! + consists of composite numbers, for any natural number . [67] However, large prime gaps occur much earlier than this argument shows. [68]
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
An odd prime number p is defined to be regular if it does not divide the class number of the pth cyclotomic field Q(ζ p), where ζ p is a primitive pth root of unity. The prime number 2 is often considered regular as well. The class number of the cyclotomic field is the number of ideals of the ring of integers Z(ζ p) up to equivalence.
Thus, all Mersenne numbers M 4k +1 are congruent to 11 modulo 20 and end in 11, 31, 51, 71 or 91, while Mersenne numbers M 4k −1 ≡ 7 (mod 20) and end in 07, 27, 47, 67, or 87. For the perfect numbers, define P n = 2 n−1 M n be the value which is perfect if M n is prime.
These numbers have been proved prime by computer with a primality test for their form, ... 67 9145334×3 9145334 + 1 25 December 2023 4,363,441 68 4×5 6181673 – 1
That is, it is a prime number of the form M n = 2 n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2 n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form M p = 2 p ...