We describe the computation which resulted in the title of this paper. Furthermore, we give an analysis of the data collected during this computation. From these data, we derive the important observation that in the final stages, the progress of the double large prime variation of the quadratic sieve integer factoring algorithm can more effectively be approximated by a quartic function of the time spent, than by the more familiar quadratic function. We also present, as an update to [15], some of our experiences with t..
It was shown in [2] that under reasonable assumptions the general number field sieve (GNFS) is the ...
We give an effective version with explicit constants of the large sieve inequality for imaginary qua...
GQS is a set of computer programs for factoring “large ” inte-gers. It is based on multiple polynomi...
We describe a modification to the well-known large prime variant of the multiple polynomial quadrati...
We present the results of many factorization runs with the single and double large prime variations ...
The quadratic sieve and the number field sieve are two traditional factoring methods. We present her...
In my last paper, I described the Quadratic Sieve (QS) and it’s variants, including a very abbreviat...
Integer factorization is a problem not yet solved for arbitrary integers. Huge integers are therefor...
We report the factorization of a 135-digit integer by the triple-large-prime variation of the multip...
Factorization of positive integers into primes is a hard computational task. Its complexity lies in ...
Prime factorization is a mathematical problem with a long history. One of the oldest known methods o...
Factoring large integers has long been a subject that has interested mathematicians. And although th...
The subject of our study is the single large prime variation of the quadratic sieve algorithm. We de...
1.1 Prime factorization and the Number Field Sieve One of the most important and widely-studied ques...
Integer factorization problem is one of the most important parts in the world of cryptography. The s...
It was shown in [2] that under reasonable assumptions the general number field sieve (GNFS) is the ...
We give an effective version with explicit constants of the large sieve inequality for imaginary qua...
GQS is a set of computer programs for factoring “large ” inte-gers. It is based on multiple polynomi...
We describe a modification to the well-known large prime variant of the multiple polynomial quadrati...
We present the results of many factorization runs with the single and double large prime variations ...
The quadratic sieve and the number field sieve are two traditional factoring methods. We present her...
In my last paper, I described the Quadratic Sieve (QS) and it’s variants, including a very abbreviat...
Integer factorization is a problem not yet solved for arbitrary integers. Huge integers are therefor...
We report the factorization of a 135-digit integer by the triple-large-prime variation of the multip...
Factorization of positive integers into primes is a hard computational task. Its complexity lies in ...
Prime factorization is a mathematical problem with a long history. One of the oldest known methods o...
Factoring large integers has long been a subject that has interested mathematicians. And although th...
The subject of our study is the single large prime variation of the quadratic sieve algorithm. We de...
1.1 Prime factorization and the Number Field Sieve One of the most important and widely-studied ques...
Integer factorization problem is one of the most important parts in the world of cryptography. The s...
It was shown in [2] that under reasonable assumptions the general number field sieve (GNFS) is the ...
We give an effective version with explicit constants of the large sieve inequality for imaginary qua...
GQS is a set of computer programs for factoring “large ” inte-gers. It is based on multiple polynomi...