M27751 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	1,070.7332	77.6119%	500000000	10000000000	0.6681	13.6287%	1,071.4013	80.6631%	3.0512%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.0226%	0.0000	64.0085%	1.5085%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7187%	0.0001	66.4950%	0.5859%
Difference	+23	+1,070.7331	+11.7028%	+499999500	+9999990000	+0.6681	+11.9100%	+1,071.4012	+14.1681%	+14.1681%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27751	45789151	8	25.449	825 3 × 5² × 11	-	25	25	1.898e-10	1.641e-8	3.340e-8
27751	4399258800137	13	42.0004	79263068 2² × 419 × 47293	2008-08-26	419	47293	3.184e-5	1.952e-6	3.160e-6
27751	554620776611591	15	48.978	9992807045 5 × 13 × 9661 × 15913	2008-08-26	9661	15913	0.0017	6.566e-6	1.291e-5
27751	95726878185821608708207	23	76.341	1724746462935058353 3 × 7 × 31 × 173 × 15314335996511	2011-03-20	173	15314335996511	884,871	547.79	1,023.1
27751	539030029339958598598400797029041	33	108.732	9711902802420788414803084520 2³ × 5 × 59 × 4115213051873215430001307	2018-03-24	59	4115213051873215430001307	5.718e+12	1.472e+14	2.749e+14

exponent	prime factors	composite factor	digits	bits*
27751	45789151 4399258800137	201438325487551913687	21	67.449
27751	45789151 554620776611591	25395614488005408649241	23	74.427
27751	4399258800137 554620776611591	2439920332247358935146587967	28	90.979
27751	45789151 95726878185821608708207	4383252480009191700203005262257	31	101.790
27751	45789151 4399258800137 554620776611591	111721880521244487632626323555746017	36	116.427
27751	4399258800137 95726878185821608708207	421127311268618329651193837364624359	36	118.342
27751	554620776611591 95726878185821608708207	53092115522023549975858947400093027337	38	125.320
27751	45789151 539030029339958598598400797029041	24681727406981794604970562453683109734191	41	134.181
27751	45789151 4399258800137 95726878185821608708207	19283062045902766257766291949358226832529209	44	143.790
27751	4399258800137 539030029339958598598400797029041	2371332600111918170539256700265003384003778617	46	150.732
27751	45789151 554620776611591 95726878185821608708207	2431042894547380155400651697203917042781020887	46	150.768
27751	554620776611591 539030029339958598598400797029041	298957253489496520436572181682659755811604214231	48	157.711
27751	4399258800137 554620776611591 95726878185821608708207	23356595642815231586505448825528904712475056034516 9	51	167.320
27751	45789151 4399258800137 539030029339958598598400797029041	10858130649774723801046577647619597996566000366438 4167	54	176.181
27751	45789151 554620776611591 539030029339958598598400797029041	13688998822575833088244789549466741640480672917659 607881	56	183.159
27751	95726878185821608708207 539030029339958598598400797029041	51599661957126064487063209526047211833993654579474 039487	56	185.073
27751	45789151 4399258800137 554620776611591 95726878185821608708207	10694786847348087042144675585949156727441319244979 555461519	59	192.769
27751	4399258800137 554620776611591 539030029339958598598400797029041	13151903282784554188280310354024501270505753681190 01760149647	61	199.711
27751	45789151 95726878185821608708207 539030029339958598598400797029041	23627047129038008928338748475328142157957223825813 78294650205537	64	210.522
27751	45789151 4399258800137 554620776611591 539030029339958598598400797029041	60221448535281765219484956112729134637487980167681 557564757969079697	68	225.159
27751	4399258800137 95726878185821608708207 539030029339958598598400797029041	22700026694898121559220658149843468558122919207416 8598262120179009719	69	227.074
27751	554620776611591 95726878185821608708207 539030029339958598598400797029041	28618244587556825471661726134094372217250684214707 858650049689195893817	71	234.052
27751	45789151 4399258800137 95726878185821608708207 539030029339958598598400797029041	10394149500367210176915101583425632081716426241492 109145282558456823053758569	77	252.522
27751	45789151 554620776611591 95726878185821608708207 539030029339958598598400797029041	13104051227745722026025649988746934577058963843605 74560613781376093850566579367	79	259.500
27751	4399258800137 554620776611591 95726878185821608708207 539030029339958598598400797029041	12589906434628243446476728440822230348758651333133 7980332802192267357605722677052929	84	276.052
27751	45789151 4399258800137 554620776611591 95726878185821608708207 539030029339958598598400797029041	57648112681106426803548333656280366959609254844921 47813493709834861069779434123700800973279	91	301.501

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-12-22T01:05:43	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 45789151 skipped known factor: 4399258800137 skipped known factor: 554620776611591	-	-	0.668	-	-	13.629%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	4399258800137	42.0004	13	1.07300e-5	2.57981e-5	2.20306e-5
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	554620776611591	48.978	15	0.000	2.57981e-5	0.001

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.776 GHz-days
Estimated T-Level:	31.617

Digits	B1	Curves	Complete	FacMiss
20	11000	1286 / 100	12.860	0.000%
25	50000	1286 / 280	4.593	1.004%
30	250000	1111 / 640	1.736	17.600%
35	1000000	511 / 1580	0.323	72.360%
40	3000000	500 / 4700	0.106	89.907%

New Calculation Method

Total ECM effort:	15.776 GHz-days
Estimated T-Level:	31.617

Digits	B1	Complete	FacMiss
20	11000	157.256	0.000%
25	50000	31.870	0.000%
30	250000	5.491	0.412%
35	1000000	0.796	45.113%
40	3000000	0.098	90.628%
45	11000000	0.011	98.945%
50	44000000	0.001	99.899%

ECM Summary

B1	B2	factor	curves	GHz-days
		95726878185821608708207	1	0.00000e+0
50000	5000000		174	0.082
200000	20000000		1	0.002
250000	25000000		600	1.417
1000000	100000000		11	0.104
3000000	300000000		382	10.83
3000000	300000000	539030029339958598598400797029041	118	3.344

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-06T12:38:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.014
2009-05-10T17:32:00	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.071
2010-04-18T20:08:00	James Hintz	10_122109	50000	5000000						3	0.001
2010-04-19T10:50:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-20T03:41:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-20T23:12:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-21T17:45:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-22T12:23:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-23T10:26:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-24T03:54:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-24T09:49:00	James Hintz	14_091909	50000	5000000						32	0.015
2010-04-24T13:12:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-04-24T23:12:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-25T15:39:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-04-25T16:49:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-04-25T18:25:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-04-25T19:00:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-25T19:19:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-04-25T21:34:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-04-25T23:20:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-04-26T20:25:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-04-26T21:41:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-05-03T15:51:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-03T18:16:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-03T21:00:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-04T16:12:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-04T20:08:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-04T22:28:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-05T16:35:00	Rob_Dee	twopc	200000	20000000						1	0.002
2010-05-05T19:10:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-05-05T23:10:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-06T17:11:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-07T16:48:00	Rob_Dee	twopc	250000	25000000						1	0.002
2011-03-20T14:32:00	James Hintz	17_051310			95726878185821608708207	76.341		1		1	-
2014-11-14T03:42:00	James Hintz	08_04_2014	250000	25000000						561	1.325
2014-11-14T04:06:00	James Hintz	08_04_2014	1000000	100000000						11	0.104
2018-03-24T09:31:36	nordi	nordiputer	3000000	300000000	539030029339958598598400797029041	108.732	118	2		118	3.344
2018-03-28T07:34:24	nordi	nordiputer	3000000	300000000						382	10.83

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:37:33

Oliver Kruse

Ollaptop

45789151

4399258800137

554620776611591

95726878185821608708207

4760CF42449C9455

2017-09-21T21:28:57

Oliver Kruse

Manual testing

45789151

4399258800137

554620776611591

95726878185821608708207

4760CF42449C9455

2017-10-02T10:28:52

kkmrkkblmbrbk

Manual testing

45789151

4399258800137

554620776611591

95726878185821608708207

4760CF42449C94__

2017-12-07T03:11:55

ATH

xps

45789151

4399258800137

554620776611591

95726878185821608708207

4760CF42449C94__

2018-03-24T09:36:51

ATH

xps

45789151

4399258800137

554620776611591

95726878185821608708207

539030029339958598598400797029041

A200A8F8C5457C__

2018-03-26T11:53:15

Oliver Kruse

GTX-4

45789151

4399258800137

554620776611591

95726878185821608708207

539030029339958598598400797029041

A200A8F8C5457C__

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront