User group for PFGW & PrimeForm programs Yahoo Group 82000-digit prime with all digits prime =============================================== David Broadhurst Message 1 of 2 Oct 20, 2003 ----------------------------------------------- N=(10^40950+1)*(10^20055+1)*(10^10374+1)* (10^4955+1)*(10^2507+1)*(10^1261+1)* (3*R(1898)+555531001*10^940-R(958))+1 is a prime all of whose 82000 decimal digits are prime. The Ansatz was selected after detailed scrutiny of the the database of factors of 10^n+1 maintained by Greg Childers. Phil Carmody sieved a range of candidates to a depth of 0.46T. OpenPFGW found that N is probably prime. VFYPR proved the primality of 238 factors of N-1 with up to 237 digits. Primo proved the primality of 9 larger factors of N-1, namely: //p713= Phi(2*955,10)/805712491/8216075917481/128275956445522068558281771 //p952= Phi(2*991,10)/154326449/1040954329/769150565783664091847 //p1148= Phi(2*1261,10)/22699 //p1416= gcd(Phi(2*5850,10),10^(4*585)+5*10^(3*585)+7*10^(2*585)+5*10^585+1\ +10^((585+1)/2)*(10^(3*585)+2*10^(2*585)+2*10^585+1))\ /13667940001/170791741656901 //p1440= gcd(Phi(2*4550,10),10^(4*455)+5*10^(3*455)+7*10^(2*455)+5*10^455+1\ +10^((455+1)/2)*(10^(3*455)+2*10^(2*455)+2*10^455+1)) //p2367= Phi(2*2507,10)/60169/65183 //p2567= Phi(2*3458,10)/20749/2074801/16204189/65321621 //p3951= Phi(2*4955,10)/6612070921 //p4560= Phi(2*6685,10) OpenPFGW performed the BLS tests: > [N-1, Brillhart-Lehmer-Selfridge] > Running N-1 test using base 3 > Running N-1 test using base 5 > Calling Brillhart-Lehmer-Selfridge with factored part 30.18% > (10^40950+1)*(10^20055+1)*(10^10374+1)* > (10^4955+1)*(10^2507+1)*(10^1261+1)* > (3*R(1898)+555531001*10^940-R(958))+1 > is PRP! (22606.887000 seconds) Pari-GP completed the Konyagin-Pomerance proof. David Broadhurst =============================================== David Broadhurst Message 2 of 2 Oct 25, 2003 ----------------------------------------------- > //p3951= > Phi(2*4955,10)/6612070921 took merely 370 hours to prove, at 1.0 Ghz: > [PRIMO - Primality Certificate] > Version=2.2.0 beta 1 > WebSite=http://www.ellipsa.net/ <snip> > Initialization=46.84s > 1stPhase=305h 7mn 29s > 2ndPhase=65h 5mn 34s > Total=370h 13mn 50s <snip> > BinarySize=13123 My old guestimator suggested (13123/3000)^4.5=765 GHz-hours. So this was twice as fast as most of my experience with versions previous to 2.2.0 beta 1. David =============================================== Cached by Georg Fischer at Nov 14 2019 12:47 with clean_yahoo.pl V1.4