Every integer greater than 1 can be written as a product of prime numbers in a unique way, except for the order of the factors. You can use our Prime Factorization Calculator to calculate the prime factorization of any number. How many prime numbers are there? According to Euclid's theore...
finished the factorization with 53,687,196 unique relations. The filtering, linear algebra and square root phases were performed at Microsoft Research Cambridge because of the very heavy memory requirements of the first two phases. The first filtering step took about 1.4 gigabytes of active memory ...
However, as this test requires a partial factorization of n - 1 the running time was still quite slow in the worst case. The first deterministic primality test significantly faster than the naive methods was the cyclotomy test; its runtime can be proven to be O((log n)c log log log n)...