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125 and 126 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur. Like many other powers of 5, it is a Friedman number in base 10 since 125 = 5 1 + 2. 125 is the center of a close triplet of perfect powers, (121 = 11 2, 125 = 5 3, 128 = 2 7). Excluding the trivial cases of 0 and 1 ...
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.
The progressions of numbers that are 0, 3, or 6 mod 9 contain at most one prime number (the number 3); the remaining progressions of numbers that are 2, 4, 5, 7, and 8 mod 9 have infinitely many prime numbers, with similar numbers of primes in each progression.
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number. For example: 7 = 7 1 , 9 = 3 2 and 64 = 2 6 are prime powers, while 6 = 2 × 3 , 12 = 2 2 × 3 and 36 = 6 2 = 2 2 × 3 2 are not.
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These numbers have been proved prime by computer with a primality test for their form, ... 125 9221×2 11392194-1 [50] 7 February 2021 3,429,397 126 9×2 11366286 +1
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