From Tetsuya Izu:
I would like to report that I have found a 61-digit prime P61 out of a 363-digit composite C363 by GMP-ECM 6.2.3 (unfortunately, C363 still has a 173-digit unfactored part): P61 = 4431999617 2455571529 8543909507 5047794565 3944486806 5870916937 7 C363 = 5038502348 5034852362 7070710808 5020385028 0879316051 3738582034 8503850234 8503485236 2707071080 8502038502 8508793160 5137385820 3485038502 3485034852 3627070710 8085020385 0285087931 6051373858 2034850385 0234850348 5236270707 1080850203 8502850879 3160513738 5820348503 8502348503 4852362707 0710808502 0385028508 7931605137 3858203485 0385023485 0348523627 0707108085 0203850285 0879316051 373 GMP-ECM parameters are as follows: GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM] Input number is 322127132059354394945399039695599969781105574731942636148174464379230078857327121374195168128302184905797178770632313914925786383448532232114872332013435149507659679760222415140060027091065515097016088056024555269261279333003265156081 (234 digits) Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=3108910259 Step 1 took 1475473ms Step 2 took 351080ms ********** Factor found in step 2: 4431999617245557152985439095075047794565394448680658709169377 Found probable prime factor of 61 digits: 4431999617245557152985439095075047794565394448680658709169377 Composite cofactor 72682120911272357689259148549732546588968300852450550995699034741070149633062411736610558028751079553975361439097957638717020236844687588444607499211555314733235516208558353 has 173 digits Here, GMP-ECM 6.2.3 has already found the following 7 small primes P2 = 23 P10 = 3993359999 P15 = 270147724086077 P18 = 105540293482603433 P21 = 122128379182503903409 P34 = 1972391254929583965677794768690457 P34 = 2479582642686043659506633342398313 and what I actually tried was the above 234-digit composite. I have to explain why I'm factoring such an unnatural composite. When I saw a TV educational program on NHK (Japan Broadcasting Corporation), on this April, which introduces PKI and RSA. As an example of the RSA 1024-composite, the program showed the above 363-digit integer (see cap001.jpg). I felt something wrong because the integer seemed longer (1205-bit in fact!) and a fixed pattern 50385023485034852362707071080850203850285087931605137385820348 is repeatedly appeared. I gave a contact to NHK and the above mistake has been removed. A natural question arose: is factoring C363 hard or not, and that's why I am factoring.