Wagstaff Sets Two World Records in Factorization

09-20-2012

Samuel Wagstaff, Professor of Computer Science and CERIAS Fellow, has set two new world records in computer-based mathematics. One of these records was achieved years before experts had predicted it would be.

Wagstaff announced record factorizations by the Elliptic Curve Integer Factoring Algorithm, primes of 79 and 75 decimal digits. Although the 75-digit prime (discovered on August 2, 2012) was no surprise, the 79-digit prime factor (found ten days later on August 12) should not have appeared for many more years.

Professor Wagstaff explains his find for number theorists at this link, and provides a less technical description at this link.

As Wagstaff's website notes, "Given the worldwide effort being made in elliptic curve factoring, a factor of 75 digits was expected to appear approximately in 2012. However, the 79-digit factor was a surprise. A prime factor that large should not have appeared for quite a few more years. Another surprise was that Professor Wagstaff had tried only a few thousand elliptic curves on the number factored when the 79-digit factor appeared. Each of these curves had roughly one chance in a million of discovering the 79-digit prime. It is as if Professor Wagstaff bought 1,000 one dollar lottery tickets once and won the million dollar prize!"

The computations were done on cores of the compute clusters Hansen and Carter in the Rosen Center for Advanced Computing at Purdue University, which were purchased in part with NFS Grant DMS-1068350, whose support is gratefully acknowledged. Professor Wagstaff's research is also supported, in part, by the Center for Education and Research in Information Assurance and Security (CERIAS).

Samuel Wagstaff has been with the Department of Computer Science since 1983. He also has a courtesy appointment in Mathematics.

Congratulations to Professor Wagstaff on setting these factorization records!