M13 451 Mersenne number exponent details

is 2 ¹³⁴⁵¹ - 1

has 4050 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	2,209.0490	79.1045%	400000000	400000000	0.1144	7.8124%	2,209.1633	80.7369%
Target	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.3836%	0.0002	68.6221%
Difference	+23	+2,209.0488	+10.9227%	+399999500	+399990000	+0.1144	+6.4288%	+2,209.1632	+12.1149%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
13451	26903	5	14.715	1 1	-	1	1	1.623e-13	2.860e-10	5.820e-10
13451	107609	6	16.715	4 2²	2008-08-26	4	4	6.496e-13	1.144e-9	2.328e-9
13451	2690201	7	21.359	100 2² × 5²	2008-08-26	25	25	2.122e-11	7.149e-9	1.455e-8
13451	25744353137	11	34.584	956968 2³ × 37 × 53 × 61	2008-08-26	53	61	1.933e-7	1.528e-8	3.085e-8
13451	7150628005253909099846161	25	82.564	265802840132849197080 2³ × 3 × 5 × 7² × 73 × 619240611622517	2009-06-09	73	619240611622517	112,535,980	9,648.1	18,020

exponent	prime factors	composite factor	digits	bits*
13451	26903 107609	2895004927	10	31.431
13451	26903 2690201	72374477503	11	36.075
13451	107609 2690201	289489839409	12	38.075
13451	26903 25744353137	692600332444711	15	49.299
13451	107609 25744353137	2770324096719433	16	51.299
13451	26903 107609 2690201	7788145149620327	16	52.790
13451	2690201 25744353137	69257484553510537	17	55.943
13451	26903 107609 25744353137	74530029174042905999	20	66.014
13451	26903 2690201 25744353137	1863234106943093976911	22	70.658
13451	107609 2690201 25744353137	7452728655318715376033	22	72.658
13451	26903 107609 2690201 25744353137	200500759014039399761415799	27	87.374
13451	26903 7150628005253909099846161	192373345225345916513161269383	30	97.280
13451	107609 7150628005253909099846161	769471929017367904325345539049	30	99.280
13451	2690201 7150628005253909099846161	19236626610362071514315242168361	32	103.924
13451	26903 107609 7150628005253909099846161	20701103306354248730064771037035247	35	113.995
13451	25744353137 7150628005253909099846161	184088292518578527216137361157757057	36	117.148
13451	26903 2690201 7150628005253909099846161	517522965698570809949622960055415983	36	118.639
13451	107609 2690201 7150628005253909099846161	2070034152914452153583948894495158849	37	120.639
13451	26903 25744353137 7150628005253909099846161	4952527333627318117695743427227138104471	40	131.863
13451	107609 25744353137 7150628005253909099846161	19809557069631716735201325296825079146713	41	133.863
13451	26903 107609 2690201 7150628005253909099846161	55690128815857506287868977108603258514647	41	135.355
13451	2690201 25744353137 7150628005253909099846161	495234508621772472495379945123959192498457	42	138.507
13451	26903 107609 25744353137 7150628005253909099846161	532936513844302075327121254460485104284019839	45	148.579
13451	26903 2690201 25744353137 7150628005253909099846161	13323293985451544827543206663669874155785988671	47	153.223
13451	107609 2690201 25744353137 7150628005253909099846161	53291690238280313992755340514844124745566459313	47	155.223
13451	26903 107609 2690201 25744353137 7150628005253909099846161	14337063424804552873470969258708514880299744548976 39	52	169.938

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: 26903 skipped known factor: 107609 skipped known factor: 2690201 skipped known factor: 25744353137	-	-	0.114	-	-	7.812%

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	?	?	107609	16.715	6	5.61962e-16	0.000	3.80940e-14
2008-08-26	ANONYMOUS	Manual testing	?	?	25744353137	34.584	11	2.31285e-8	0.000	1.56485e-6
2008-08-26	ANONYMOUS	Manual testing	?	?	2690201	21.359	7	4.49570e-13	0.000	3.04752e-11

ECM factoring results:

Total ECM effort:	22.502 GHz-days
Estimated T-Level:	36.917

Digits	B1	Complete	FacMiss
20	11000	551.674	0.000%
25	50000	124.090	0.000%
30	250000	21.915	0.000%
35	1000000	3.170	4.201%
40	3000000	0.383	68.148%
45	11000000	0.040	96.035%
50	44000000	0.004	99.627%

ECM Summary

B1	B2	factor	curves	GHz-days
		7150628005253909099846161	1	0.00000e+0
50000	5000000		91	0.019
250000	25000000		551	0.567
500000	50000000		10	0.021
1000000	100000000		1,421	5.848
3000000	300000000		1,300	16.05

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-07	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.010
2009-06-07	unconnected	dual5430	250000	25000000						30	0.031
2009-06-09	Rob_Dee	twopc			7150628005253909099846161	82.564		1		1	-
2009-06-09	Rob_Dee	twopc	50000	5000000						23	0.005
2009-07-07	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-07	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-08	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-08	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-09	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-21	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-24	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-28	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-31	Rob_Dee	twopc	500000	50000000						5	0.010
2009-08-10	Rob_Dee	twopc	500000	50000000						5	0.010
2010-05-29	James Hintz	home2	250000	25000000						481	0.495
2010-12-30	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-09	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-11	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-14	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-17	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-20	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-24	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-27	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-31	James Hintz	newestmember	1000000	100000000						3	0.012
2011-03-31	James Hintz	newestmember	1000000	100000000						3	0.012
2011-04-10	James Hintz	17_051310	1000000	100000000						11	0.045
2014-05-28	BloodIce	Mjolnir4	1000000	100000000						502	2.066
2014-05-30	BloodIce	Mjolnir4	1000000	100000000						607	2.498
2014-06-01	BloodIce	Mjolnir4	1000000	100000000						271	1.115
2014-06-01	BloodIce	Mjolnir4	3000000	300000000						100	1.235
2014-06-03	BloodIce	Mjolnir4	3000000	300000000						200	2.469
2021-10-05	nordi	sweet16	3000000	300000000						1000	12.35

Lucas-Lehmer results:
No L-L results for M13451

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

26903

107609

2690201

25744353137

7150628005253909099846161

CD982DF83F2E5C95

2017-09-21

Oliver Kruse

Manual testing

26903

107609

2690201

25744353137

7150628005253909099846161

CD982DF83F2E5C95

2017-10-02

kkmrkkblmbrbk

Manual testing

26903

107609

2690201

25744353137

7150628005253909099846161

CD982DF83F2E5C__

2017-12-07

ATH

Manual testing

26903

107609

2690201

25744353137

7150628005253909099846161

CD982DF83F2E5C__

2020-04-17

Oliver Kruse

Manual testing

26903

107609

2690201

25744353137

7150628005253909099846161

94404714DDBD51__

2022-05-12

Jorge Coveiro

Manual testing

26903

94404714DDBD5138

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

10¹⁴

10¹⁵

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=36.92 ~= 106-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2023-03-23T17:39:31+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