M21013 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	1,414.0731	77.6119%	500000000	10000000000	0.4722	13.3828%	1,414.5452	80.6081%	2.9961%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	3.7442%	0.0000	63.9041%	1.4041%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.5826%	0.0001	66.4486%	0.5395%
Difference	+23	+1,414.0730	+11.7028%	+499999500	+9999990000	+0.4722	+11.8002%	+1,414.5451	+14.1595%	+14.1595%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
21013	120477000381373968760623607	27	86.639	2866725369565839450831 3 × 19 × 317 × 105882607 × 1498398557	2014-04-23	105882607	1498398557	1.480e+9	0.0843	0.1000
21013	14537445072856023012177419127481	32	103.520	345915506421168396044767980 2² × 3 × 5 × 5765258440352806600746133	2017-10-06	5	5765258440352806600746133	8.252e+12	1.457e+14	2.722e+14
21013	262993879056590526599462437387619513220841	42	137.594	6257885096287786765322953347632882340 2² × 3 × 5 × 59 × 242399 × 7292786486304502390480104379	2022-01-31	242399	7292786486304502390480104379	8.212e+12	1.844e+17	3.443e+17

exponent	prime factors	composite factor	digits	bits*
21013	120477000381373968760623607 14537445072856023012177419127481	17514277755866782075127734209550691048439202753033 91043967	58	190.158
21013	120477000381373968760623607 262993879056590526599462437387619513220841	31684713667399876288686814656540415971887832375043 403756708268993487	68	224.233
21013	14537445072856023012177419127481 262993879056590526599462437387619513220841	38232590712825247725694866138351597301687322579677 75181020343554285031521	73	241.114
21013	120477000381373968760623607 14537445072856023012177419127481 262993879056590526599462437387619513220841	46061478458899622263992646564252531303139448680495 7678616645815979948100529194528808326309611716247	99	327.753

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-04-29T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.000	-	-	1.842%
2001-08-18T00:00:00	Alex Kruppa	v4_computers	1000000	100000000		-		-	-	0.003	-	-	4.560%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	4.86067e-5	-	-	0.604%
2002-06-09T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	9.72135e-5	-	-	0.981%
2002-07-20T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.000	-	-	1.478%
2003-02-02T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.000	-	-	2.099%
2003-03-27T00:00:00	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.001	-	-	2.837%
2003-04-03T00:00:00	ANONYMOUS	v4_computers	524288	52428800		-		-	-	0.002	-	-	3.683%
2003-04-27T00:00:00	ANONYMOUS	v4_computers	1048576	104857600		-		-	-	0.003	-	-	4.628%
2003-05-19T00:00:00	ANONYMOUS	v4_computers	2097152	209715200		-		-	-	0.006	-	-	5.665%
2003-07-06T00:00:00	ANONYMOUS	v4_computers	4194304	419430400		-		-	-	0.012	-	-	6.787%
2003-09-29T00:00:00	ANONYMOUS	v4_computers	8388608	838860800		-		-	-	0.025	-	-	7.989%
2003-09-29T00:00:00	ANONYMOUS	v4_computers	16777216	1677721600		-		-	-	0.050	-	-	9.256%
2016-11-19T00:49:55	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 120477000381373968760623607	-	-	0.472	-	-	13.383%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-11-28T00:00:00	eteo	v4_computers	?	?	120477000381373968760623607	86.639	27	734,660,293	1.39205e-5	1.52091e+9
1999-10-15T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.029	-	-
2000-03-01T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.057	-	-
2000-08-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.457	-	-
2002-11-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.914	-	-
2022-06-16T04:12:24	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.914	-	-
2022-06-16T04:12:24	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	1.827	-	-
2022-06-16T04:12:24	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	3.655	-	-
2022-06-15T12:07:01	LordJulius	Whitebox_TF	2⁵⁹	2⁶⁰		-	-	3.655	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	100.100 GHz-days
Estimated T-Level:	39.361

Digits	B1	Curves	Complete	FacMiss
20	11000	6008 / 100	60.080	0.000%
25	50000	6008 / 280	21.457	0.000%
30	250000	5878 / 640	9.184	0.010%
35	1000000	5423 / 1566	3.463	3.130%
40	3000000	4002 / 4588	0.872	41.796%

New Calculation Method

Total ECM effort:	100.100 GHz-days
Estimated T-Level:	39.361

Digits	B1	Complete	FacMiss
20	11000	1,092.697	0.000%
25	50000	282.205	0.000%
30	250000	53.108	0.000%
35	1000000	8.190	0.028%
40	3000000	1.046	35.139%
45	11000000	0.115	89.126%
50	44000000	0.011	98.895%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		130	0.043
250000	25000000		455	0.759
1000000	100000000		992	6.623
1000000	100000000	14537445072856023012177419127481	429	2.864
3000000	300000000		400	8.012
3000000	413502526		380	8.548
3000000	415344231		380	8.564
3000000	416576122		380	8.574
3000000	418430129		380	8.589
3000000	419049774		1,140	25.78
3000000	419091626		380	8.594
3000000	419670247		380	8.599
3000000	528000000	262993879056590526599462437387619513220841	182	4.547

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-03T13:21:00	Matthias Wurtinger	AMD_Funzel	50000	5000000						30	0.010
2009-06-01T17:55:00	GrunwalderGIMP	GWPrime02	50000	5000000						100	0.033
2009-06-12T19:40:00	unconnected	dual5430	250000	25000000						30	0.050
2011-04-01T19:02:00	James Hintz	17_051310	250000	25000000						11	0.018
2014-10-08T21:12:00	James Hintz	08_04_2014	250000	25000000						414	0.691
2014-10-08T21:31:00	James Hintz	08_04_2014	1000000	100000000						11	0.073
2017-10-06T18:08:10	kkmrkkblmbrbk	r4.4xlarge-8	1000000	100000000	14537445072856023012177419127481	103.520	429	2		429	2.864
2017-10-07T14:38:05	kkmrkkblmbrbk	r4.4xlarge-8	1000000	100000000						981	6.550
2021-10-12T23:09:08	nordi	sweet16	3000000	300000000						400	8.012
2022-01-31T10:19:12	fbaur	Manual testing	3000000	528000000	262993879056590526599462437387619513220841	137.594	182	2	6108330422011107	182	4.547
2022-01-31T17:59:00	fbaur	Manual testing	3000000	419091626						380	8.594
2022-01-31T17:59:00	fbaur	Manual testing	3000000	419670247						380	8.599
2022-01-31T17:59:00	fbaur	Manual testing	3000000	419049774						380	8.594
2022-01-31T17:59:00	fbaur	Manual testing	3000000	418430129						380	8.589
2022-01-31T17:59:00	fbaur	Manual testing	3000000	416576122						380	8.574
2022-01-31T17:59:00	fbaur	Manual testing	3000000	413502526						380	8.548
2022-01-31T17:59:01	fbaur	Manual testing	3000000	415344231						380	8.564
2022-01-31T18:51:39	fbaur	Manual testing	3000000	419049774						380	8.594
2022-01-31T18:51:52	fbaur	Manual testing	3000000	419049774						380	8.594

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:26:17

Oliver Kruse

Oliver-PC

120477000381373968760623607

212E564C42A1CB__

2017-09-21T20:26:58

Oliver Kruse

Manual testing

120477000381373968760623607

212E564C42A1CB__

2017-10-07T01:10:10

Oliver Kruse

GTX-0

120477000381373968760623607

14537445072856023012177419127481

52BAD031B5AEB4C7

2017-10-15T17:17:56

YarBer

Manual testing

120477000381373968760623607

14537445072856023012177419127481

2017-10-16T13:19:20

Oliver Kruse

Threadripper

120477000381373968760623607

14537445072856023012177419127481

52BAD031B5AEB4__

2020-04-17T13:48:58

Oliver Kruse

Manual testing

120477000381373968760623607

14537445072856023012177419127481

9CE865A7FCF442__

2022-01-31T10:19:12

fbaur

Manual testing

120477000381373968760623607

14537445072856023012177419127481

262993879056590526599462437387619513220841

9CE865A7FCF442E0

2022-02-01T05:35:19

LordJulius

surface7

120477000381373968760623607

14537445072856023012177419127481

262993879056590526599462437387619513220841

9CE865A7FCF442E0

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 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

B1 = 16777216, B2 = 1677721600 (P-1 stage 2)

B1 = 8388608, B2 = 838860800 (P-1 stage 2)

B1 = 4194304, B2 = 419430400 (P-1 stage 2)

B1 = 16777216 (P-1 stage 1)

B1 = 2097152, B2 = 209715200 (P-1 stage 2)

B1 = 8388608 (P-1 stage 1)

B1 = 1048576, B2 = 104857600 (P-1 stage 2)

B1 = 1000000, B2 = 100000000 (P-1 stage 2)

B1 = 4194304 (P-1 stage 1)

B1 = 524288, B2 = 52428800 (P-1 stage 2)

B1 = 2097152 (P-1 stage 1)

B1 = 262144, B2 = 26214400 (P-1 stage 2)

B1 = 1048576 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 100000, B2 = 10000000 (P-1 stage 2)

B1 = 524288 (P-1 stage 1)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 262144 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

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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