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The smallest pair of consecutive Achilles numbers ... The integer 500 = 2 2 × 5 3 is a strong Achilles number as its Euler totient of 200 = 2 3 × 5 2 is also an ...
The smallest such number is 25326001. This means that, if n is less than 25326001 and n is a strong probable prime to bases 2, 3, and 5, then n is prime. Carrying this further, 3825123056546413051 is the smallest number that is a strong pseudoprime to the 9 bases 2, 3, 5, 7, 11, 13, 17, 19, and 23.
A prime number (or prime) is a ... Integers R n that are the smallest to give at least n primes from x/2 to x for all x ... Strong prime; Table of prime factors;
72 is the sum between 60 and 12, the former being the second unitary perfect number before 6 (and the latter the smallest of only two sublime numbers). More specifically, twelve is also the number of divisors of 60, as the smallest number with this many divisors. [19] 72 is the number of distinct {7/2} magic heptagrams, all with a magic ...
A powerful number is a positive integer m such that for every prime number p dividing m, p 2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a 2 b 3, where a and b are positive integers. Powerful numbers are also known as squareful, square-full, or 2-full.
The strong Goldbach conjecture is much more ... One record from this search is that 3 325 581 707 333 960 528 is the smallest number that cannot be written as a sum ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
There is also overlap among strong pseudoprimes to different bases. For example, 1373653 is the smallest strong pseudoprime to bases 2 through 4, and 3215031751 is the smallest strong pseudoprime to bases 2 through 10. Arnault [11] gives a 397-digit Carmichael number N that is a strong pseudoprime to all prime bases less than 307.