The nth Prime Page will now find any of the first 2.623˙1015 primes or π(x) for x up to 1017.
Any integer greater than one is called a prime number if (and only if) its only positive divisors (factors) are one and itself.
The number of factors of an integer can be found by adding 1 to the exponent of each prime factor and then calculating the product. For example, the prime factorization of 12 is 22 * 3 and 12 has (2 + 1)(1 + 1) = 6 factors.
The chance of a random integer x being prime is about 1/log(x).
Bertrand's postulate asserts the existence of at least one prime between n and 2n.
Mersenne primes can be written as unbroken strings of consecutive 1s in binary form.
The only number with exactly one positive divisor. [Gupta]
The only number whose concatenation with itself can yield primes in many cases. [Murthy]
There is only 1 "Prime Street" in England. It is in Stoke-on-Trent, Staffordshire. [Croll]
Bertrand's Postulate guarantees that in every base there is at least one prime of any given length beginning with the digit 1, and Benford's Law tells us that primes with leading digit 1 occur more often than primes beginning with any other digit in all bases. [Rupinski]
Carl Sagan included the number 1 in an example of prime numbers in his book Cosmos.
The smallest number n such that 10n + 1, 10n + 3, 10n + 7 and 10n + 9 are all primes. [Firoozbakht]
(1) = !1, where !1 denotes subfactorial 1. [Gupta]
The only number that is exactly 1/2 prime. [McAlee]
If primes were called pints, then we could say, "1 is a half-pint." [McAlee]
1 is the only positive integer whose primal code characteristic is 1. [Awbrey]
The number 1 is an "extinct" prime since it was once thought to be prime by many and now is no longer considered to be prime. [Hilliard]
The number of primes between two squares is never equal to 1. [Capelle]
(There are 14 curios for this number that have not yet been approved by an editor.)
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