M8 737 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	67000000000	265422648792401100	2,556,989.7800	80.0566%	2,556,989.7800	80.0566%
Target	2⁴⁴	0.0003	68.1818%	500	50000	0.0000	1.2123%	0.0003	68.5676%
Difference	-44	-0.0003	-68.1818%	+66999999500	+265422648792351100	+2,556,989.7800	+78.8443%	+2,556,989.7797	+11.4890%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8737	681487	6	19.378	39 3 × 13	-	3	13	8.062e-12	6.268e-10	1.080e-9
8737	6640121	7	22.663	380 2² × 5 × 19	-	5	19	6.921e-11	1.019e-9	1.799e-9
8737	5724729222836153	16	52.346	327614125148 2² × 19 × 4310712173	-	19	4310712173	0.0893	0.0415	0.0776
8737	30427637033372331604582934081	29	94.619	1741309204153160787717920 2⁵ × 5 × 1415411 × 7689061711373767	-	1415411	7689061711373767	6.162e+11	74,073	138,349
8737	297225269049958516065232816142632074242944393961	48	157.702	17009572453356902601878952509020949653367540 2² × 5 × 17 × 23 × 12041647 × 86109467 × 798912559 × 2625733247123117	2023-08-08	798912559	2625733247123117	1.511e+13	25,295	47,245

exponent	prime factors	composite factor	digits	bits*
8737	681487 6640121	4525156139927	13	42.041
8737	681487 5724729222836153	3901328543882941399511	22	71.724
8737	6640121 5724729222836153	38012894731868019094513	23	75.009
8737	681487 6640121 5724729222836153	25905293592136540728662380831	29	94.387
8737	681487 30427637033372331604582934081	20736039078961810148212409998058447	35	113.998
8737	6640121 30427637033372331604582934081	202043191645673319906554836832863801	36	117.282
8737	681487 6640121 30427637033372331604582934081	137689808545034973763158336088717853152087	42	136.660
8737	5724729222836153 30427637033372331604582934081	174189982906798135931395447044167249062630393	45	146.965
8737	681487 5724729222836153 30427637033372331604582934081	11870820888120514126147888901978840606194479863439 1	51	166.344
8737	6640121 5724729222836153 30427637033372331604582934081	11566425634890713451589134672223628780130023877975 53	52	169.628
8737	681487 297225269049958516065232816142632074242944393961	20255515692904907923774731617459390437960144620730 0007	54	177.081
8737	6640121 297225269049958516065232816142632074242944393961	19736117507492795916535897923578302314541341721727 09281	55	180.365
8737	681487 6640121 5724729222836153 30427637033372331604582934081	78823687066447676379831246203696641064844695825299 1001311	57	189.007
8737	681487 6640121 297225269049958516065232816142632074242944393961	13449907511828743010772299468245606509429835345914 63129780847	61	199.743
8737	5724729222836153 297225269049958516065232816142632074242944393961	17015341834956354951983247238885717703291675362040 77712185672033	64	210.048
8737	681487 5724729222836153 297225269049958516065232816142632074242944393961	11595734261078901467162207211086511100463133967451 08307844277076753071	70	229.427
8737	6640121 5724729222836153 297225269049958516065232816142632074242944393961	11298392864047222660011795163911707072169882269666 956702316036765435993	71	232.711
8737	681487 6640121 5724729222836153 297225269049958516065232816142632074242944393961	76997078577409496289034582508686975174918365583085 25322191248947166678561591	76	252.089
8737	30427637033372331604582934081 297225269049958516065232816142632074242944393961	90438626037985728318881688297120751260466538013613 34922719241604471757484841	76	252.322
8737	681487 30427637033372331604582934081 297225269049958516065232816142632074242944393961	61632747942748780034849725112539929414241559591283 32052479167803306644593071838567	82	271.700
8737	6640121 30427637033372331604582934081 297225269049958516065232816142632074242944393961	60052341996597583231050099497716573998040032886149 228608381413281926610781999905761	83	274.984
8737	681487 6640121 30427637033372331604582934081 297225269049958516065232816142632074242944393961	40924890390235297203378639156400374864202307891483 179356640024193260320201992769777346607	89	294.363
8737	5724729222836153 30427637033372331604582934081 297225269049958516065232816142632074242944393961	51773664535280750940359481604624046351808853104839 905128989638394434097972470368159924256673	92	304.668
8737	681487 5724729222836153 30427637033372331604582934081 297225269049958516065232816142632074242944393961	35283079323154873116092762040290427476155159875858 032426639761700507710124964913786202301907312751	98	324.046
8737	6640121 5724729222836153 30427637033372331604582934081 297225269049958516065232816142632074242944393961	34378339712767295521485074135197782728561935348736 2655685011806685288137063057913496444415143777433	99	327.330
8737	681487 6640121 5724729222836153 30427637033372331604582934081 297225269049958516065232816142632074242944393961	23428391595834645923050298717173531358339487635004 23141348116411025369566626921482949514151430874514 82871	105	346.709

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-12-16	Lisander Viaene	Desktop	100000000	100000000		-	skipped known factor: 681487 skipped known factor: 6640121	-	-	0.018	-	-	26.318%
2023-08-08	JacobZ	GreatLakes	67000000000	265422648792401100			297225269049958516065232816142632074242944393961	48	157.702	2,556,990	2.13086e-6	5,113,980	80.057%

ECM factoring results:

Total ECM effort:	801.813 GHz-days
Estimated T-Level:	43.227

Digits	B1	Complete	FacMiss
20	11000	1,983.800	0.000%
25	50000	549.120	0.000%
30	250000	137.253	0.000%
35	1000000	26.914	0.000%
40	3000000	4.458	1.159%
45	11000000	0.645	52.442%
50	44000000	0.083	92.074%
55	110000000	0.010	99.050%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		3,919	29.91
11000000	36578884662		2,400	771.9

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.008
2013-04-18	Axon		3000000	300000000						30	0.229
2018-06-07	James Hintz	3_1_2018	3000000	300000000						3888	29.68
2021-01-10	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

DC37C2A0F4F014__

2017-09-21

Oliver Kruse

Manual testing

DC37C2A0F4F014__

2017-10-02

kkmrkkblmbrbk

Manual testing

681487

6640121

5724729222836153

30427637033372331604582934081

DC37C2A0F4F014__

2017-12-07

ATH

Manual testing

681487

6640121

5724729222836153

30427637033372331604582934081

DC37C2A0F4F014__

2020-04-17

Oliver Kruse

Manual testing

681487

6640121

5724729222836153

30427637033372331604582934081

63A257186720BB__

2023-08-08

JacobZ

GreatLakes

681487

6640121

5724729222836153

30427637033372331604582934081

297225269049958516065232816142632074242944393961

63A257186720BB89

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 67000000000, B2 = 265422648792401100 (P-1 stage 2)

B1 = 67000000000 (P-1 stage 1)

B1 = 100000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=43.23 ~= 127-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

2¹⁶⁰

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