M553363 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	53.6970	70.1493%	15000000	1815000000	2.3909	12.1602%	56.0879	73.7791%	3.6299%
PrimeNet	2⁴⁰	0.0000	50.0000%	5500	190000	0.0003	19.7854%	0.0003	59.8927%	9.8927%
GPU72	2⁴⁴	0.0000	54.5455%	10000	320000	0.0006	14.9963%	0.0006	61.3619%	6.8165%
Difference	+23	+53.6970	+15.6038%	+14990000	+1814680000	+2.3904	-2.8361%	+56.0873	+12.4172%	+12.4172%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
553363	23491802846165153503	20	64.349	21226394650677 3 × 439 × 16117232081	2009-10-30	439	16117232081	10.462	18.568	34.681
553363	243576699733039119911	21	67.723	220087627590785 5 × 47 × 936543096131	2016-03-18	47	936543096131	55.860	1,079.0	2,015.2

exponent	prime factors	composite factor	digits	bits*
553363	23491802846165153503 243576699733039119911	5722055808048123382564655642195338698233	40	132.072

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.536%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.184%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.790%
2002-09-07T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.535%
2003-05-11T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.409%
2016-03-17T18:48:40	alpertron	Manual testing	1500000	50000000	12	-		-	-	0.088	-	-	6.167%
2021-08-27T16:36:26	ViliamF	3	15000000	1815000000		-		-	-	2.391	-	-	12.160%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.004	-	-
2022-03-07T08:27:09	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.017	-	-
2002-01-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.035	-	-
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.069	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.130 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	422 / 100	4.220	1.439%
25	50000	422 / 280	1.507	22.095%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	16.130 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.783	0.000%
25	50000	3.017	4.892%
30	250000	0.286	75.100%
35	1000000	0.022	97.835%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		23491802846165153503	1	0.00000e+0
50000	5000000		220	3.556
50000	5000000	243576699733039119911	58	0.937
250000	25000000		144	11.64

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-19T22:42:00	drew	messier	50000	5000000						1	0.016
2007-09-25T03:30:00	Chad Davis	Bayes	50000	5000000						1	0.016
2008-01-14T12:36:00	Steve Scott	Gigabyte-2	50000	5000000						3	0.048
2008-08-15T16:41:00	Sturle Sunde	v17	50000	5000000						3	0.048
2008-10-22T17:52:00	Sturle Sunde	v23	50000	5000000						3	0.048
2008-12-25T02:02:00	Sturle Sunde	v23	50000	5000000						3	0.048
2009-02-28T21:18:00	Sturle Sunde	v23	50000	5000000						3	0.048
2009-04-10T14:51:00	Lupo	yorick	50000	5000000						3	0.048
2009-07-02T02:36:00	Architects Cubed	m1_41	50000	5000000						3	0.048
2009-07-10T19:08:00	Architects Cubed	m1_62	50000	5000000						3	0.048
2009-08-09T21:46:00	JimBa	NASsrvr	50000	5000000						3	0.048
2009-09-19T11:48:00	David Bessell	L301	50000	5000000						3	0.048
2009-10-14T14:19:00	JimBa	ISAserv	50000	5000000						3	0.048
2009-10-30T10:50:00	JimBa	ISAserv			23491802846165153503	64.349		1		1	-
2015-07-24T08:19:00	TJAOI	Manual testing	50000	5000000						62	1.002
2016-03-18T10:46:47	TJAOI	Manual testing	50000	5000000						32	0.517
2016-03-18T10:46:47	TJAOI	Manual testing	50000	5000000	243576699733039119911	67.723	58	2		58	0.937
2016-09-30T22:09:08	TJAOI	Manual testing	50000	5000000						91	1.471
2018-12-14T12:17:52	TJAOI	Manual testing	250000	25000000						44	3.556
2020-10-30T10:27:54	TJAOI	Manual testing	250000	25000000						100	8.081

date	userid	compid	res64	spent (GHz-days)
2002-05-11T00:00:00	ANONYMOUS	v4_computers	FE9C4E10382D6500	0.008

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T10:51:08

Oliver Kruse

GTX-1

23491802846165153503

243576699733039119911

97DBF828EFF3CF91

2017-09-28T09:43:13

Oliver Kruse

Manual testing

23491802846165153503

243576699733039119911

97DBF828EFF3CF__

2017-10-13T15:20:29

kkmrkkblmbrbk

c4.xlarge

97DBF828EFF3CF__

2020-04-19T06:36:24

Oliver Kruse

AddPrpType5

23491802846165153503

243576699733039119911

494A3EE3DE18EB__

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 = 15000000, B2 = 1815000000 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

B1 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

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

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

B1 = 100000, B2 = 4000000 (P-1 stage 2)

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