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Old 2013-02-26, 02:04   #650
LaurV
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Here's a good one: 12395067022025302245408215823361, 104 bits.
(from which you can see that not all prime exponents containing the "number of the best" will generate prime mersennes )
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Old 2013-02-26, 02:40   #651
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Quote:
Originally Posted by LaurV View Post
Here's a good one: 12395067022025302245408215823361, 104 bits.
(from which you can see that not all prime exponents containing the "number of the best" will generate prime mersennes )
"number of the BEAST"
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Old 2013-02-26, 03:22   #652
LaurV
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Quote:
Originally Posted by c10ck3r View Post
"number of the BEAST"
grrr, typo, thanks
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Old 2013-02-27, 11:13   #653
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M95516249819281897377329792747204747051937323318703014161875271870743369159415765467622402105668679795781959994061775011707821819120345026036123142898041417744024085438782757861002649408975294945304266551957165557916259132607823871 has a factor: 191032499638563794754659585494409494103874646637406028323750543741486738318831530935244804211337359591563919988123550023415643638240690052072246285796082835488048170877565515722005298817950589890608533103914331115832518265215647743
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Old 2013-02-27, 15:16   #654
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Quote:
Originally Posted by jnml View Post
M95516249819281897377329792747204747051937323318703014161875271870
7433691594157654676224021056686797957819599940617750117078218191203450260361231428980
41417744024085438782757861002649408975294945304266551957165557916259132607823871 has a factor: 191032499638563794754659585494409494103874646637406028323750543741486738318831530935244
804211337359591563919988123550023415643638240690052072246285796082835488048170877565515
722005298817950589890608533103914331115832518265215647743
I'm just curious. How did you get these two numbers? And what's special of the exponent?

Last fiddled with by dabaichi on 2013-02-27 at 15:21 Reason: format
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Old 2013-02-27, 15:43   #655
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Quote:
Originally Posted by dabaichi View Post
I'm just curious. How did you get these two numbers? And what's special of the exponent?
Nothing special above the fact that both the factor and the exponent are PRPs. Otherwise it's a 2p+1 | Mp (i.e. k == 1), so I actually cheated (in a sense).

Got that from a toy program of mine, it's just the size surprised me a bit ;-)

Code:
(16:38) jnml@fsc-r550:~/src/tmp/mersenne/ff$ time ./ff
2: 23 | M11 (5 bits)
2: 47 | M23 (6 bits)
2: 383 | M191 (9 bits)
14: 479 | M239 (9 bits)
20: 167 | M83 (8 bits)
26: 863 | M431 (10 bits)
26: 7421703487487 | M3710851743743 (43 bits)
26: 143556623544770914273611162510277214207 | M71778311772385457136805581255138607103 (127 bits)
32: 263 | M131 (9 bits)
32: 290271069732863 | M145135534866431 (49 bits)
44: 359 | M179 (9 bits)
44: 719 | M359 (10 bits)
44: 1439 | M719 (11 bits)
44: 2879 | M1439 (12 bits)
44: 23039 | M11519 (15 bits)
44: 1474559 | M737279 (21 bits)
44: 2949119 | M1474559 (22 bits)
44: 24159191039 | M12079595519 (35 bits)
44: 6184752906239 | M3092376453119 (43 bits)
50: 52223 | M26111 (16 bits)
56: 1823 | M911 (11 bits)
56: 3825205247 | M1912602623 (32 bits)
62: 503 | M251 (9 bits)
62: 191032499638563794754659585494409494103874646637406028323750543741486738318831530935244804211337359591563919988123550023415643638240690052072246285796082835488048170877565515722005298817950589890608533103914331115832518265215647743 | M95516249819281897377329792747204747051937323318703014161875271870743369159415765467622402105668679795781959994061775011707821819120345026036123142898041417744024085438782757861002649408975294945304266551957165557916259132607823871 (765 bits)
^C
real	0m31.379s
user	0m31.070s
sys	0m0.080s
(16:38) jnml@fsc-r550:~/src/tmp/mersenne/ff$
EDIT: The code is now available here.

Last fiddled with by jnml on 2013-02-27 at 16:03
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Old 2013-02-27, 18:31   #656
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factor5 confirm the factor found.
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Old 2013-02-27, 20:22   #657
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Quote:
Originally Posted by firejuggler View Post
factor5 confirm the factor found.
Thanks for the confirmation. Are such "factors" worth of reporting here? For example:

Code:
jnml@fsc-r630:~/src/github.com/cznic/mathutil/ff$ time ./ff -c 1382 -d 10s
1382: 23202889727 | M11601444863 (35 bits)
1382: 2891317468805925583122310289685036337676269648223968521576930801170224130471293604830368928083599358133453548705464010629846117567184743543864401985621482209720123399448999256896093377478118494454636064824009640486909425185943889123952719307865058813784823875371947571635800099775698380593420250938639525924694459005059051692445445662364099847064237399153239430674586254346911706508030497459384755111708766149920027758576898244058419917181406937087 | M1445658734402962791561155144842518168838134824111984260788465400585112065235646802415184464041799679066726774352732005314923058783592371771932200992810741104860061699724499628448046688739059247227318032412004820243454712592971944561976359653932529406892411937685973785817900049887849190296710125469319762962347229502529525846222722831182049923532118699576619715337293127173455853254015248729692377555854383074960013879288449122029209958590703468543 (1487 bits)
^C
real	0m6.973s
user	0m6.816s
sys	0m0.060s
jnml@fsc-r630:~/src/github.com/cznic/mathutil/ff$
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Old 2013-02-27, 20:49   #658
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I'm afraid that the range considered usefull are only the M below 100 millions and the range
between 332.2 -334 millions. Outside of these range, it is not really usefull (outside of personnal quest).

Last fiddled with by firejuggler on 2013-02-27 at 20:49
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Old 2013-02-27, 21:21   #659
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Quote:
Originally Posted by jnml View Post
Nothing special above the fact that both the factor and the exponent are PRPs. Otherwise it's a 2p+1 | Mp (i.e. k == 1), so I actually cheated (in a sense). ...
Thanks for your explanations!
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Old 2013-02-28, 04:26   #660
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59933213 haz dat factor of teh 266130256367911424981339321 87.78 bitz.
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