News

Leyland and Hoogendoorn GNFS the C135 —Finishes M(1485), M(2970), & M(5940)

November 14, 2005: Paul Leyland and Sander Hoogendoorn teamed up to factor the smallest ElevenSmooth composite, a C135 from M(1485), into P61 x P75. The factors are on the factors page,http://home.earthlink.net/~elevensmooth/ElevenFactors.html . They used the General Number Field Sieve, sharing the polynomial search and sieving with Paul doing the post processing. Additional information is available on the forum thread, http://www.mersenneforum.org/showthread.php?t=4855 , where they originated and coordinated this project.

ElevenSmooth had previously found two factors for this Mersenne number. These factors complete the factorization of M(1485). M(1485) is an algebraic factor, http://home.earthlink.net/~elevensmooth ... #Algebraic , of M(2970) and M(5940). Thanks to three other factors previously found by ElevenSmooth, their factorizations are now complete, too.

Congratulations to Sander and Paul!

Karli finds another P35

Karli Lopez has found a P35 factor of M(47520). This is the second ElevenSmooth factor for Karli; the other was a 35 digit factor of M(15840). This is the third factor that ElevenSmooth has found for the primitive part of M(47520). The remaining unfactored C3386 continues in the ECM Server.