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Thread: Factor bragging

  1. #41
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    3593405260603031 | 10223*2^5774585+1

    3593405260603030 = 2*5*31*3187*16573*219463

  2. #42
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    15799176637249321 | 4847*2^6001023+1

    15799176637249320 = 2 ^ 3 x 3 ^ 2 x 5 x 7 x 47 x 1163 x 3137 x 36563

  3. #43
    Senior Member dmbrubac's Avatar
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    5720000 -> 5730000 had 5 factors:

    13860049223357177 | 55459*2^5720278+1
    13860049223357176 = 2^3*7*823*1361*1657*133351

    52252110283617819719 | 10223*2^5725757+1
    see previous post

    2408494707706313 | 67607*2^5726411+1
    2408494707706312=2^3*353*1597*9041*59069

    1990620885055391 | 21181*2^5726972+1
    1990620885055390=2*5*7*41*2351*4483*65809

    363916348856369 | 24737*2^5727391+1
    363916348856368=2^4*7*11*19^2*14891*54949

  4. #44
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    407337342926141 | 21181*2^5777180+1

    407337342926140 = 2 ^ 2 x 5 x 11 x 31 x 41 ^ 2 x 59 ^ 3 x 173



    Does anyone have smoother P-1?

  5. #45
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    Originally posted by Nuri
    407337342926141 | 21181*2^5777180+1

    407337342926140 = 2 ^ 2 x 5 x 11 x 31 x 41 ^ 2 x 59 ^ 3 x 173



    Does anyone have smoother P-1?
    Well you still have to have B1 >= 1681 (41^2) and B2 >= 205379 (59^3) to find that, so I don't really know if it counts as smooth.

  6. #46
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    To be honest, I do not know much about the theory (or math) behind it, so I'll take your word for the concept of smoothness. (I previously thought it meant having many small prime factors for P-1).

    But, there's something I do not get. I used B1=10000 and B2=65000 (That's the first k/n pair after I switched to lower settings of 1.25x and 160MB to keep up with PRP).

  7. #47
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    Originally posted by Nuri
    To be honest, I do not know much about the theory (or math) behind it, so I'll take your word for the concept of smoothness. (I previously thought it meant having many small prime factors for P-1).

    But, there's something I do not get. I used B1=10000 and B2=65000 (That's the first k/n pair after I switched to lower settings of 1.25x and 160MB to keep up with PRP).
    Smooth means that all the factors are small. What I don't remember is whether it's 59 or 59^3 you have to consider a factor.

    As for the bounds it would be possible to find the factor if the factorer doesn't only try primes (and prime powers) between B1 and B2. Whether that or something I can't think of is the explanation, we have to hear Louie about, since he's probably the only one knowing that part of the code well enough.

  8. #48
    Originally posted by hc_grove
    As for the bounds it would be possible to find the factor if the factorer doesn't only try primes (and prime powers) between B1 and B2. Whether that or something I can't think of is the explanation, we have to hear Louie about, since he's probably the only one knowing that part of the code well enough. [/B]
    Stage 2 does drag in some composite numbers between B1 and B2. So I think stage 1 caught the 59^2 and stage 2 picked up the other 59 in a composite number between B1 and B2.

  9. #49
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    5740000 -> 5745000 gave me

    9422557846421851 | 28433*2^5741185+1
    9422557846421850=2*3^9*5^2*13*17*29*89*113*108287

    249632915700529 | 10223*2^5743901+1
    249632915700528=2^4*3^3*1399*2027*203773

    but this is real bragging
    Attached Images Attached Images

  10. #50
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    A pretty smooth factor:

    322163790109561 | 19249*2^5763038+1

    322163790109560 = 2^3*3^3*5*7*107*113*1637*2153

  11. #51
    Senior Member Frodo42's Avatar
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    Just found a factor in a range beings fast-checked (factor value 1.2)
    1172536902962371 | 19249*2^5794718+1

    It seems to me that we are having trouble keeping up with PRP, and I'm being closed in by priwo if I don't find some more factors fast I only have something like 1:15 of his factors in store so I have to keep finding P-1-factors to stay in the race.

  12. #52
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    Exclamation I did it again

    My newest factor:

    220516583040629 | 28433*2^5840545+1

    220516583040628 = 2^2*7*127*1879*2113*15619

    Once again, this is a factor that Mystwalker will find in his sieving range

  13. #53
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    I found 233793054676939 | 4847*2^5884647+1 today through sieving.

    Unfortunately, it turned out to be a duplicate of 173003399270327 | 4847*2^5884647+1.

    I guess the chances of such a thing to happen is really low (i.e. ~1 out of every 5.200 factors => to find a factor through sieving that's in the active range is 200k/19m and ratio of duplicates is currently at 1.8%).

    Last edited by Nuri; 03-22-2004 at 02:03 PM.

  14. #54
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    1185354900631669 | 55459*2^5843506+1

    1185354900631668 = 2^2*3*13*5557*6949*196771

  15. #55
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    246188828265473 | 10223*2^5796845+1
    246188828265472 = 2^10*53*97*2111*22153

    171388807977727 | 21181*2^5797244+1
    171388807977726 = 2*3^2*83*139*6247*132113

    437621215726002191369 | 4847*2^5803263+1 <-- the new 2nd largest factor of the year
    437621215726002191368=2^3*43*211*227*7127*19441*191693

    2015485189907779 | 4847*2^5801991+1
    2015485189907778=2*7*263*17921*3054449

    5172107658035209 | 21181*2^5804804+1 <-- submitted about an hour before it would have gone to PRP
    5172107658035208=2^3*3*11*16193*19759*61231
    Last edited by dmbrubac; 03-30-2004 at 11:06 AM.

  16. #56
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    21143274634835342257 | 55459*2^5890846+1


    21143274634835342256 = 2 ^ 4 x 3 x 23 x 31 x 3119 x 4021 x 4091 x 12041

  17. #57
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    It's been more than a week since the last one, but now I found:
    16865935315528471 | 10223*2^5884637+1
    284817113042325587201 | 55459*2^5874526+1
    1927699125194094887 | 22699*2^5874598+1


    16865935315528470 = 2*3*5*17*113*4483*5791*11273
    (second one is larger than 2^64, I will factor that tomorrow).
    1927699125194094886 = 2*653*709*1259*11467*144203

  18. #58
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    Originally posted by hc_grove
    284817113042325587201 | 55459*2^5874526+1

    (second one is larger than 2^64, I will factor that tomorrow).
    284 817113 042325 587200 = 2 ^ 8 x 5 ^ 2 x 37 x 43 x 89 x 547 x 2333 x 246277



    And found one myself:
    2918283220459681 | 55459*2^5868118+1

    2918 283220 459680 = 2 ^ 5 x 3 x 5 x 29 x 509 x 6011 x 68521

  19. #59
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    Originally posted by Mystwalker
    284 817113 042325 587200 = 2 ^ 8 x 5 ^ 2 x 37 x 43 x 89 x 547 x 2333 x 246277
    Thanks. Now 2^8 that's something I haven't seen before.

  20. #60
    Senior Member dmbrubac's Avatar
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    I had a 2^10 a few days back (see my previous post).

  21. #61
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    8057451392817109 | 10223*2^5869769+1
    8057 451392 817108 = 2 ^ 2 x 3 x 29 x 31 x 59 x 71 ^ 2 x 347 x 7237

  22. #62
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    3796805718943647229 | 24737*2^5951647+1

    3796805718943647228 = 2^2*3^2*7*13*41*47*193*22751*136973

  23. #63
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    3025213428395171034079 | 28433*2^6051073+1

    3025213428395171034078 = 2*3*43*83*353*367*599*7907*230239

  24. #64
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    3492869317679191 | 24737*2^6053911+1

    3492869317679190 = 2*3*5*613*3251*3389*17239

  25. #65
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    Just found my first one with self-compiled factorer:

    260840209049520371 | 21181*2^6103172+1

    260840209049520370 = 2 x 5 x 179 x 367 x 1217 x 4363 x 74779
    not very smooth (even though I don't really understand that term) but that counts in favor for the program.

  26. #66
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    65922812594639417 | 33661*2^6055008+1

    65922812594639416 = 2^3*13^2*23*103*1483*1949*7121

  27. #67
    Senior Member Frodo42's Avatar
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    oh boy oh boy oh boy

    just found a big one
    35935660269812747397727 | 4847*2^6168951+1

    It's definetly the largest for 4847 so far, not all that smooth (or is it?)
    35935 660269 812747 397726 = 2 x 3 ^ 2 x 19 x 29 x 367 x 2707 x 4651 x 5273 x 148711

  28. #68
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    It's been three weeks, but I finally found a new factor:
    501737316342481 | 33661*2^6280416+1
    501737316342480 = 2^4*3^4*5*19*47*317*273521

    Apart from the last factor this is the smoothest I've seen.

  29. #69
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    Ahh, only two days.

    5274028739098589 | 4847*2^6281463+1
    5274028739098588 = 2^2*7*167*877*16993*75683

  30. #70
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    235703760784331778069847 | 19249*2^6405242+1

    235703760784331778069846 = 2 x 3 x 11 x 13 ^ 2 x 17 x 389 x 1427 x 2521 x 2791 x 318259

  31. #71
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    Very smooth - apart from the last 'bummer'...

  32. #72
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    6258055154249506859 | 4847*2^6508047+1

    6258055154249506858 = 2 x 19 x 577 x 811 x 1151 x 14759 x 20717

  33. #73
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    622529950198081 | 55459*2^6821266+1

    622529950198080 = 2^6*3*5*73*83*401*266897

    Apart from the last factor this is extremely smooth.

    But the main "feature" of this factor is that I used George's new factoring code to find it!

  34. #74
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    11529059469964763 | 28433*2^6989137+1
    11529059469964762 = 2 x 11 x 67 x 167 x 1787 x 4817 x 5441

    10340964718983403 | 55459*2^6990238+1
    10340964718983402 = 2 x 3 x 7 x 41 x 83 x 401 x 457 x 394811

    1405455930948721 | 55459*2^6990250+1
    1405455930948720 = 2 ^ 4 x 3 x 5 x 7 x 31 x 47 x 7793 x 73679

  35. #75
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    524413893207156299 | 10223*2^6705785+1

    524413893207156298 = 2 x 17 ^ 2 x 1091 x 1693 x 18287 x 26861

    Would have been a B1 hit...

  36. #76
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    75249573592556119391 | 24737*2^6826063+1

    75249573592556119390 = 2*5*43*557*1031*4111*4507*16447

    Fairly smooth.

    Would have been a stage 1 factor, but I used Georges new code.

  37. #77
    So does George's new code not do a GCD at the end of stage 1??

  38. #78
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    Originally posted by garo
    So does George's new code not do a GCD at the end of stage 1??
    Depends on the setting of the ini file. I switched it off, as I think most factors will be found in the B2 stage...

  39. #79
    Well then it's a bit unfair to "blame" George's code for not finding it in stage 1. At least that's what hc_grove's post in particular and your post to some extent indicated.

  40. #80
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    I'd rather say these postings were a bit misleading.
    Of course, George's new algorithm would also find it with GCD after stage 1.

    P.S.: If I can't blame George's code, I can blame himself for giving the tip to switch off stage 1 GCD.

    Ouch! Don't beat me again! Ouch!

    I hope you can forgive us.

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