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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. Subsets of the prime numbers may be generated with various formulas for primes.
A prime number is a natural number that has exactly two distinct natural number divisors: the number 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method: Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n). Initially, let p equal 2, the smallest prime number.
43 is the smallest number with the property 43 = 4*prime(4) + 3*prime(3). Where prime(n) is the n-th prime number. There are only two numbers with that property, the other one is 127. 43 is a Gaussian prime. When taking the first six terms of the Taylor series for computing e, one obtains
73 has 37 as the mirroring of its decimal digits. 73 is the 21st prime number, and 37 the 12th. The "mirror property" is fulfilled when 73 has a mirrored permutation of its digits (37) that remains prime. Similarly, their respective prime indices (21 and 12) in the list of prime numbers are also permutations of the same digits (1, and 2).
is a prime number for all positive natural numbers n. This constant is named after William Harold Mills who proved in 1947 the existence of A based on results of Guido Hoheisel and Albert Ingham on the prime gaps. [1] Its value is unproven, but if the Riemann hypothesis is true, it is approximately 1.3063778838630806904686144926...
"Seventh prime number") The clue may require arithmetic to be applied to another answer or answers (e.g. "25 across times 3" or "9 down minus 3 across") The clue may indicate possible answers but make it impossible to give the correct one without using crosslights (e.g. "A prime number")
However, it does not contain all the prime numbers, since the terms gcd(n + 1, a n) are always odd and so never equal to 2. 587 is the smallest prime (other than 2) not appearing in the first 10,000 outcomes that are different from 1. Nevertheless, in the same paper it was conjectured to contain all odd primes, even though it is rather inefficient.
A prime number is called a digitally delicate prime number when, under a given radix but generally decimal, replacing any one of its digits with any other digit always results in a composite number. [1] A weakly prime base-b number with n digits must produce () composite numbers after every digit is individually changed to every other digit ...