M15 739 Mersenne number exponent details

is 2 ¹⁵⁷³⁹ - 1

has 4738 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	1,887.9165	79.1045%	400000000	400000000	0.1382	7.9146%	1,888.0547	80.7583%
Target	2⁴⁴	0.0001	68.1818%	500	10000	0.0000	1.4511%	0.0001	68.6435%
Difference	+23	+1,887.9163	+10.9227%	+399999500	+399990000	+0.1382	+6.4635%	+1,888.0546	+12.1148%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15739	168627647	9	27.329	5357 11 × 487	-	11	487	1.317e-9	1.276e-8	1.701e-8
15739	662915222009	12	39.270	21059636 2² × 13 × 173 × 2341	2008-08-26	173	2341	6.341e-6	1.006e-7	1.217e-7
15739	8508927323826791	16	52.918	270313467305 5 × 7 × 19 × 29² × 483337	2008-08-26	841	483337	0.0575	9.375e-6	1.700e-5
15739	6402822397968242369	19	62.473	203406264628256 2⁵ × 6356445769633	2008-08-29	32	6356445769633	46.270	119.68	223.53
15739	64895190524604148223	20	65.815	2061604629411149 17 × 29³ × 4972358873	2008-08-29	24389	4972358873	848.82	0.0936	0.1749

exponent	prime factors	composite factor	digits	bits*
15739	168627647 662915222009	111785834047860282823	21	66.599
15739	168627647 8508927323826791	1434840393110918801890777	25	80.247
15739	168627647 6402822397968242369	1079692875128282291410175743	28	89.803
15739	662915222009 8508927323826791	5640697445933083391227043119	28	92.188
15739	168627647 64895190524604148223	10943123279780693121283721281	29	93.144
15739	662915222009 6402822397968242369	4244528431433315140577155099321	31	101.743
15739	662915222009 64895190524604148223	43020009633934312096092387840007	32	105.085
15739	8508927323826791 6402822397968242369	54481150451682153113108909263507879	35	115.391
15739	8508927323826791 64895190524604148223	552188459839749700042854585342442393	36	118.733
15739	168627647 662915222009 8508927323826791	951177537746605571717396723924510993	36	119.517
15739	6402822397968242369 64895190524604148223	415512379411351892811581223793664660287	39	128.288
15739	168627647 662915222009 6402822397968242369	715744842017200769564999886352551527687	39	129.073
15739	168627647 662915222009 64895190524604148223	7254362998487674401327697256071792873529	40	132.414
15739	168627647 8508927323826791 6402822397968242369	9187028206520148671357280223841836601730713	43	142.721
15739	168627647 8508927323826791 64895190524604148223	93114240683330988987182367889456749964639271	44	146.062
15739	662915222009 8508927323826791 6402822397968242369	36116383946982605158479723072614162289405708911	47	154.661
15739	168627647 6402822397968242369 64895190524604148223	70066874839507514773813156117706085171251154689	47	155.617
15739	662915222009 8508927323826791 64895190524604148223	366054135445475452966900104256388836245888227537	48	158.003
15739	662915222009 6402822397968242369 64895190524604148223	27544948124496418075801173817751312148185417065658 3	51	167.558
15739	8508927323826791 6402822397968242369 64895190524604148223	35355646385615366727981218087812709938171551198443 49017	55	181.206
15739	168627647 662915222009 8508927323826791 6402822397968242369	60902208431282494578044977989465363257386177220288 62417	55	181.991
15739	168627647 662915222009 8508927323826791 64895190524604148223	61726847534789822430067533464809534173212445234564 915439	56	185.332
15739	168627647 662915222009 6402822397968242369 64895190524604148223	46448397889708940400506195807254105987110221994956 036350201	59	194.887
15739	168627647 8508927323826791 6402822397968242369 64895190524604148223	59619394581703739383815618663416966535673841609335 5580983472999	63	208.535
15739	662915222009 8508927323826791 6402822397968242369 64895190524604148223	23437796172991909258561621101064609065874914526244 07630128635915153	67	220.476
15739	168627647 662915222009 8508927323826791 6402822397968242369 64895190524604148223	39522604195172306083087607707780742217533548328866 5833437438181691942034991	75	247.805

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 168627647 skipped known factor: 662915222009 skipped known factor: 8508927323826791	-	-	0.138	-	-	7.915%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26	ANONYMOUS	Manual testing	?	?	662915222009	39.270	12	1.68806e-6	0.000	6.63553e-5
2008-08-26	ANONYMOUS	Manual testing	?	?	8508927323826791	52.918	16	0.019	7.85392e-6	0.041

ECM factoring results:

Total ECM effort:	52.693 GHz-days
Estimated T-Level:	38.597

Digits	B1	Complete	FacMiss
20	11000	368.435	0.000%
25	50000	104.637	0.000%
30	250000	23.831	0.000%
35	1000000	4.467	1.148%
40	3000000	0.719	48.704%
45	11000000	0.101	90.368%
50	44000000	0.013	98.744%
55	110000000	0.001	99.859%

ECM Summary

B1	B2	factor	curves	GHz-days
		6402822397968242369	1	0.00000e+0
		64895190524604148223	1	0.00000e+0
50000	5000000		148	0.037
250000	25000000		571	0.710
1000000	100000000		311	1.547
3000000	300000000		45	0.671
10000000	1000000000		1,000	49.73

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-29	ANONYMOUS	Manual testing			64895190524604148223	65.815		1		1	-
2008-08-29	ANONYMOUS	Manual testing			6402822397968242369	62.473		1		1	-
2009-04-07	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.012
2009-06-08	unconnected	dual5430	250000	25000000						30	0.037
2009-06-12	Rob_Dee	twopc	50000	5000000						80	0.020
2009-07-04	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-05	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-05	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-05	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-06	Rob_Dee	twopc	250000	25000000						10	0.012
2010-04-08	James Hintz	17_012210	250000	25000000						11	0.014
2010-08-12	Never Odd Or Even	Lap_Dir_1500	1000000	100000000						300	1.492
2010-08-19	James Hintz	home2	250000	25000000						520	0.646
2011-02-20	Never Odd Or Even	Ctower	10000000	1000000000						1000	49.73
2011-04-07	James Hintz	17_051310	1000000	100000000						11	0.055
2019-11-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-15	MarkS	laptop64	3000000	300000000						3	0.045
2019-11-15	MarkS	laptop64	3000000	300000000						3	0.045
2019-11-15	MarkS	laptop64	3000000	300000000						3	0.045
2019-11-15	MarkS	laptop64	3000000	300000000						3	0.045
2019-11-15	MarkS	laptop64	3000000	300000000						3	0.045
2019-11-15	MarkS	laptop64	3000000	300000000						3	0.045
2019-11-15	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045

Lucas-Lehmer results:
No L-L results for M15739

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

168627647

662915222009

8508927323826791

6402822397968242369

64895190524604148223

D20B109323914632

2017-09-21

Oliver Kruse

Manual testing

168627647

662915222009

8508927323826791

6402822397968242369

64895190524604148223

D20B109323914632

2017-10-02

kkmrkkblmbrbk

Manual testing

168627647

662915222009

8508927323826791

6402822397968242369

64895190524604148223

D20B1093239146__

2017-12-07

ATH

Manual testing

168627647

662915222009

8508927323826791

6402822397968242369

64895190524604148223

D20B1093239146__

2020-04-17

Oliver Kruse

Manual testing

168627647

662915222009

8508927323826791

6402822397968242369

64895190524604148223

37DA1E47AD57B3__

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 = 400000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=38.6 ~= 112-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

Last modified: 2023-03-25T13:08:14+00:00

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