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 2005-12-26, 09:32 #1 AntonVrba     Jun 2005 2×72 Posts ?? Status Factoring of (10^49081-1)/9 - 1 Is anybody trying to factor (10^49081-1)/9 - 1 so that the PRP repunit(49801) is proven prime. see http://primes.utm.edu/top20/page.php?id=57 Is there a site collecting repunit(49801) factors? Regards Anton Last fiddled with by AntonVrba on 2005-12-26 at 09:32
 2005-12-26, 09:37 #2 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts
 2005-12-30, 04:18 #3 PBMcL     Jan 2005 2×31 Posts Algebraic factorization of (10^49081-1)/9-1 For anyone interested, this is the current status as far as I've been able to piece it together, using the Cunningham tables (http://homes.cerias.purdue.edu/~ssw/cun/index.html), Alex Kruppa's page (http://home.in.tum.de/~kruppa/ecm.html), Yousuke Koide's page (http://www.h4.dion.ne.jp/~rep/), plus Pollard's p-1 method using GMP-ECM 6.0.1 to fill in some blanks when I had no other info (B1 = 1e7, default B2). I'm pretty sure that I only re-found known factors and make no claim otherwise. Using difference of squares, (10^49081-1)/9-1 factors into four major pieces: (10^49081-1)/9-1 = 2*5*[(10^6135-1)/9]*(10^6135+1)*(10^12270+1)*(10^24540+1) In Cunningham notation, 10^6135-1 factors algebraically as follows: Code: n 10^n - 1 ---------------- 1 3*3 3 (1) 3.37 5 (1) 41.271 15 (1,3,5) 31.2906161 409 (1) 1637.13907.77711.1375877.2777111.5371851809.7061270715258437. .230703986686330645437422372795294965009. C320 1227 (1,3,409) 3334987.22123889761.P800 2045 (1,5,409) 110431.163601.1265039515351. C1610 6135 (1,3,5,15,409,1227,2045) P3265 The P3265 factor of 10^6135-1 is in Chris Caldwell's Top 5000 prime list at http://primes.utm.edu/primes/lists/all.txt The three factors of the form 10^n + 1 factor algebraically as follows: Code: n 10^n + 1 ---------------- 1 11 3 (1) 7.13 5 (1) 9091 15 (1,3,5) 211.241.2161 409 (1) 53171.1358791302758702868906124409. C377 1227 (1,3,409) 1008741241.7833811446444211. .1070453760938027595699552600393152583819019423. C747 2045 (1,5,409) 4091.18601321.31661908159577184611. .86626333310030790682115011. C1576 6135 (1,3,5,15,409,1227,2045) 49081.674851.394308721. C3245 2 101 6 (2) 9901 10 (2) L.M L 3541 M 27961 30 (2,6) L.M L (10L) 61.4188901 M (10M) 39526741 818 (2) 4909.16361.2396741.34876249.2091195610248881. .4829616990104344590241.2605270211162934136387269445121.P727 2454 (2,6,818) 171989618618641.2292131539445740454732936329. C1591 4090 (2,818) L.M L (10L) 417181. C1627 M (10M) 43398572923881255601. C1612 12270 (2,6,818,2454) L.M L (10L,30L,4090L) 687121.7572258721.1495049855581. C3236 M (10M,30M,4090M) C3265 Note: 10^10h+1=(10^2h+1)L.M, L=A-B, M=A+B, h=2k-1, A = 10^4h+5*10^3h+7*10^2h+5*10^h+1, B = 10^k*(10^3h+2*10^2h+2*10^h+1). 4 73.137 12 (4) 99990001 20 (4) 1676321.5964848081 60 (4,12,20) 100009999999899989999000000010001 1636 (4) 18598049.8890622777.24801610931723485669544849. C1590 4908 (4,12,1636) 9817.1059411433.prp3251 8180 (4,20,1636) 822449921. C6520 24540 (4,12,20,60,1636,4908,8180) 23295192018739681. C13040 The prp3251 factor of 10^4908+1 is almost certainly prime but I don't know if this has been proven. If anyone has more recent info please chime in!
2006-04-14, 23:26   #4
XYYXF

Jan 2005
Minsk, Belarus

24×52 Posts

Quote:
 P727 and P800 were proven prime using F. Morain's ECPP program, P3251 and P3265 were proven prime via M. Martin's Titanix by de Water/Dubner and Broadhurst/de Water respectively.

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