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Old 2005-12-26, 09:32   #1
AntonVrba
 
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Default ?? 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
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Old 2005-12-26, 09:37   #2
akruppa
 
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See http://home.in.tum.de/~kruppa/ecm.html

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Old 2005-12-30, 04:18   #3
PBMcL
 
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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!
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Old 2006-04-14, 23:26   #4
XYYXF
 
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http://groups.yahoo.com/group/primenumbers/message/7943

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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