Primality testing (15679^3499-1)/15678 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file dls15679.fac trial factoring to 4347665 Running N-1 test using base 11 Running N+1 test using discriminant 17, base 2+sqrt(17) Calling N-1 BLS with factored part 35.60% and helper 0.04% (106.85% proof) (15679^3499-1)/15678 is prime! (357.340000 seconds) helper: << 1332739 2495771 2534179 14869273 87164543 169093321 280581131119 372774240191 17519242514363 91406600732767 5960137883285191 346202087001776149 435072602647142021 1415697491214452543 14916118119135592943 402840969336893209981 20226331972667674284313 8760627760529248288064629 103003372673620241811483109 427076727834949318967389561 732214945285216501464215071 106744947338847372498642633384301856553513388747357 806111098417221911672523514114196605081493825576615584527263711415679802498015587201 659053137617121450190295257168746231713856492732807257124627217596054023087285069433053901679808737603323425042651073506255502118326482181091630327 15376545960439194720127746549110733638112194646739432468467394719724695761443459264912845116497748441911303473683802086593403767711278162449245819371667429493039354824020720955509194229077290178626838353586621 phi(1749,15679)/(3499*1332739) >> Titanix batch file for small primes: == BPI:B28A704DCF75E ============================================ TITANIX 1.0 - Batch Processing Report Number(s) to process: 25 #1 ..... Certified (21 bits, 68ms) #2 ..... Certified (22 bits, 28ms) #3 ..... Certified (22 bits, 27ms) #4 ..... Certified (24 bits, 28ms) #5 ..... Certified (27 bits, 27ms) #6 ..... Certified (28 bits, 28ms) #7 ..... Certified (39 bits, 27ms) #8 ..... Certified (39 bits, 41ms) #9 ..... Certified (44 bits, 28ms) #10 .... Certified (47 bits, 41ms) #11 .... Certified (53 bits, 69ms) #12 .... Certified (59 bits, 55ms) #13 .... Certified (59 bits, 54ms) #14 .... Certified (61 bits, 69ms) #15 .... Certified (64 bits, 82ms) #16 .... Certified (69 bits, 54ms) #17 .... Certified (75 bits, 82ms) #18 .... Certified (83 bits, 123ms) #19 .... Certified (87 bits, 124ms) #20 .... Certified (89 bits, 124ms) #21 .... Certified (90 bits, 137ms) #22 .... Certified (167 bits, 439ms) #23 .... Certified (279 bits, 1s) #24 .... Certified (488 bits, 14s) #25 .... Certified (692 bits, 1mn 3s) Processed: 25 / 25 Certified: 25 / 25 Running time 1mn 18s ================================================================= Primo certificate for p4354=phi(1749,15679)/(3499*1332739) in http://physics.open.ac.uk/~dbroadhu/cert/p4354.zip