… factorization factory approach in order to simultaneously factor seventeen radix-2 repunits,
so-called Mersenne … First we present the theoretical analysis of the factorization factory with a …

… factor of Mersenne numbers with a prime exponent, we propose an inverse factorization
algorithm to obtain both the exponent and another factor of the minimum Mersenne number with …

… of the large number's prime factorization. The largest such … A prime can generate a large
mersenne prime by using the … number which is very difficult to factories. Now read the plaintext …

… Lenstra used this idea and managed to factor 17 Mersenne numbers [30]. Coppersmith’s
idea … 3.2 A baseline: Factory algorithm for prime fields The factorization Factory algorithm was …

… : the factorization of RSA-240, a 795-bit number, and a discrete logarithm computation over a
795-bit prime field. Previous records were the factorization … harder than a factorization of the …

… factorization of a positive integer n. The first step is to learn whether n is prime. If it is prime,
no factoring is needed. If n is composite and factorization … many large Mersenne numbers 2p …

… Also, as we will see below, a partial factorization of numbers … The reader is no doubt familiar
with the stories of Mersenne's … this rather general definition unsatisfactory, since Atlantic City …

… and resulting algorithmic changes compared to the factorization of a 768-bit RSA modulus,
… (such as Mersenne or Fermat numbers) compared to general ones (such as RSA moduli). …

The number field sieve is the best-known algorithm for factoring integers and solving the
discrete logarithm problem in prime fields. In this paper, we present some new improvements to …

… If ab, are primes (or prime power), then the factorization is called prime factorization of n.
Note that integer factorization of a number is not unique, but the prime factorization of n is …