Reserved for MF - Sequence 4788

[10metreh]

Originally Posted by Raman

To come up to a conclusion, the next iteration will acquire up the factor 3 if and only if
the c121 splits up into two (1 mod 3) factors.
Does not pick up a 3, when the c121 splits up into two (2 mod 3) factors.

Right, man?

Correct.

[Raman]

Originally Posted by 10metreh

Correct.

Meanwhile, pray up to God that it splits up into two (2 mod 3) factors

I wonder whether you check up the residue class of each factor of each iteration mod 3, 5, 7...?

Once it acquires up a factor of 3, in order to lose it up:
s(c) = product of (1+p)'s - c.
(1+p) is replaced up by (1+p+p²+...) for the prime powers...

Since c is divisible by 3, in order to lose the 3, the products of (1+p)'s should be 1 or 2 mod 3. The factor of 3 will not stimulate again a 3 in the next line at all, since (1+3+9+...) is always equal to 1 mod 3.

Any of the others should not be divisible by 3 at all.
A prime of 2 mod 3, will induce up a 3 in the next line by using (1+p)
A prime of 1 mod 3, will not.
However, that all of the primes other than 3, cannot be equal to 0 mod 3, anyway.

For the prime powers, power of 2 mod 3 will trigger up a 3 if the power is odd. Power of 1 mod 3 will trigger 3, if the power is even.

I see that it can lose up the 3 within the next iteration, if for all the primes besides 3, the power of 2 mod 3 primes are all even, and then the power of 1 mod 3 primes are all odd.
Or, in fact it is true that it can lose up the 3 within the subsequent iterations by means of using the factor of 9 = 3²

All these are natural processes only, by itself. We can't do anything to change sequences, or write up a random number of our own. We just simply compute the results, and then go on processing with the single correct number of the next iteration.

[Andi47]

Originally Posted by Andi47

Thanks. I will do a p-1 followed by GNFS

edit: started p-1 and polsel in parallel

p-1 to B1=1e9, B2=1e15 and 3* p+1 to B1=1e9, B2=1e15: no factor. Starting GNFS...

[Andi47]

Fri Dec 25 20:39:10 2009  
Fri Dec 25 20:39:10 2009  
Fri Dec 25 20:39:10 2009  Msieve v. 1.43
Fri Dec 25 20:39:10 2009  random seeds: e4aca9c8 a1f403b9
Fri Dec 25 20:39:10 2009  factoring 3942887076714143202481073805784961368619711215403426727623016228578779996971144714931046107405659926915911799176550312767 (121 digits)
Fri Dec 25 20:39:12 2009  no P-1/P+1/ECM available, skipping
Fri Dec 25 20:39:12 2009  commencing number field sieve (121-digit input)
Fri Dec 25 20:39:12 2009  R0: -220525782874300519278221
Fri Dec 25 20:39:12 2009  R1:  10561525245991
Fri Dec 25 20:39:12 2009  A0:  13919992851438837656957797344
Fri Dec 25 20:39:12 2009  A1: -7900337548465327330903242
Fri Dec 25 20:39:12 2009  A2:  14318233152048859923
Fri Dec 25 20:39:12 2009  A3: -542592852133532
Fri Dec 25 20:39:12 2009  A4: -1569762856
Fri Dec 25 20:39:12 2009  A5:  7560
Fri Dec 25 20:39:12 2009  skew 191636.60, size 1.651620e-11, alpha -6.880605, combined = 2.901254e-10
Fri Dec 25 20:39:12 2009  
Fri Dec 25 20:39:12 2009  commencing relation filtering
Fri Dec 25 20:39:12 2009  estimated available RAM is 1985.8 MB
Fri Dec 25 20:39:12 2009  commencing duplicate removal, pass 1
Fri Dec 25 20:39:28 2009  error -15 reading relation 1477379
Fri Dec 25 20:39:48 2009  error -15 reading relation 3405784
Fri Dec 25 20:40:45 2009  found 1083950 hash collisions in 8438938 relations
Fri Dec 25 20:41:14 2009  added 58146 free relations
Fri Dec 25 20:41:14 2009  commencing duplicate removal, pass 2
Fri Dec 25 20:41:20 2009  found 771129 duplicates and 7725955 unique relations

<snip>

Fri Dec 25 20:46:42 2009  matrix is 636031 x 636258 (183.2 MB) with weight 47730814 (75.02/col)
Fri Dec 25 20:46:42 2009  sparse part has weight 41667595 (65.49/col)
Fri Dec 25 20:46:42 2009  matrix includes 64 packed rows
Fri Dec 25 20:46:42 2009  using block size 65536 for processor cache size 4096 kB
Fri Dec 25 20:46:46 2009  commencing Lanczos iteration (2 threads)
Fri Dec 25 20:46:46 2009  memory use: 181.3 MB
Fri Dec 25 20:46:54 2009  linear algebra at 0.2%, ETA 0h55m
Fri Dec 25 21:46:41 2009  lanczos halted after 10061 iterations (dim = 636028)
Fri Dec 25 21:46:43 2009  recovered 27 nontrivial dependencies
Fri Dec 25 21:46:43 2009  BLanczosTime: 3718
Fri Dec 25 21:46:43 2009  
Fri Dec 25 21:46:43 2009  commencing square root phase
Fri Dec 25 21:46:43 2009  reading relations for dependency 1
Fri Dec 25 21:46:43 2009  read 317038 cycles
Fri Dec 25 21:46:44 2009  cycles contain 1023738 unique relations
Fri Dec 25 21:46:58 2009  read 1023738 relations
Fri Dec 25 21:47:06 2009  multiplying 1023738 relations
Fri Dec 25 21:50:41 2009  multiply complete, coefficients have about 44.49 million bits
Fri Dec 25 21:50:42 2009  initial square root is modulo 2443927
Fri Dec 25 21:57:45 2009  sqrtTime: 662
Fri Dec 25 21:57:45 2009  prp49 factor: 1614394407529950231948689326128270361414761568603
Fri Dec 25 21:57:45 2009  prp73 factor: 2442331971867286584011502653002290013163478345321068635697408534391895789
Fri Dec 25 21:57:45 2009  elapsed time 01:18:35

I can't post the factors to the DB right now - DB seems to be down.

Edit: If I see correctly, the factors are 1 mod 3.

[10metreh]

The 3 has disappeared again!

[Andi47]

DB is up again, and I see that someone seems to have clicked Quick-ECM - we now have a c161, and the sequence got rid of the 3 *very* quick

2495.   221665515240712835146632915038654332249677600521866315490705901031882614988052048857984072398217318255693431659468618236169689657416113688944691446324158756073966101682032 = 2^4 * 3559 * 220681 * 592772569 * 7547146554874360724158181221231 * 1614394407529950231948689326128270361414761568603 * 2442331971867286584011502653002290013163478345321068635697408534391895789
2496.   207934041439159666402719289421731533248712421461988300495417637950528851328183231602527567551285460133911968968270227215739684980733388937486979959359115607573614923085968 = 2^4 * 3^3 * 317 * 757 * 50924647 * 3088726995612795721 * 12752024987120885573855872723202403795026326832056826089540602758711687497126775191275849808610417125744238645554854915822786087517285333
2497.   391587407602724606683481473757692838731899590545814526536499415906443230131930260643701621866514302532389288790656571729396302031661198446031414125384098925446994919996272 = 2^4 * 3 * 83257 * 97986607633273229949504114208037772282385562811989413937291412910837134348045374724172747703525004537253446354524887729509306032240832213815708720534033906420029477
2498.   620025545710327153129359405293175458009270700840661687036785632653736058180215403645660032042696216110178993345887532990955937370744895402744252179739502852162138050639904 = 2^5 * 61 * 10404019

Edit: 10metreh was faster.

[R. Gerbicz]

now only c134:

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2243524066
Step 1 took 18205ms
Step 2 took 12262ms
********** Factor found in step 2: 1053510145349455459655189063
Found probable prime factor of 28 digits: 1053510145349455459655189063
Composite cofactor 2897943480588228707823873533626392259113337697364013323014773796420074066675329471987609206871621029590
2512926053853268268773796067441 has 134 digits

[R. Gerbicz]

Killed.

Run 45 out of 948:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2841086046
Step 1 took 13931ms
Step 2 took 9625ms
********** Factor found in step 2: 275672488609181335964910240943
Found probable prime factor of 30 digits: 275672488609181335964910240943
Probable prime cofactor 10512269451365601486564964719249900397856401577901033520503299884146118828035871491891733785832743
0257887 has 105 digits

[Mini-Geek]

Index 2501 has a c166. No idea how much ECM so far, but I've clicked two Quick ECMs.

[R. Gerbicz]

Factored.

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=843301289
Step 1 took 18580ms
Step 2 took 12230ms
********** Factor found in step 2: 21576911035234107060567359
Found probable prime factor of 26 digits: 21576911035234107060567359
Probable prime cofactor 27324997159006699095076661613314836247165012351115938582637324350291992335079286058776193292444980
2628020051974483243245518676185344336490951 has 141 digits

[R. Gerbicz]

Another easy goal on line 2502:

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2863442735
Step 1 took 15163ms
Step 2 took 10280ms
********** Factor found in step 2: 62867187091895665602431325293
Found probable prime factor of 29 digits: 62867187091895665602431325293
Probable prime cofactor 10388219128879144885656371803679068375540698889290568480135606623289797480435783087640389370988520
407960455115608852781 has 119 digits