M1725233 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	2⁶⁸	34.5489	69.1176%	3642200	123456789	0.8000	7.9630%	35.3489	71.5768%	2.4592%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7949%	0.0123	64.1876%	1.0297%
GPU72	2⁶¹	0.1781	65.5738%	7000	110000	0.0010	1.3445%	0.1790	66.0366%	0.4629%
Difference	+7	+34.3708	+3.5439%	+3635200	+123346789	+0.7990	+6.6185%	+35.1698	+5.5402%	+5.5402%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1725233	23780918273974220957487863	26	84.298	6892088858135168107 7 × 729969497 × 1348801733	2020-03-21	729969497	1348801733	2,893,704	60.073	116.86

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:42:00	Carsten Kossendey	leela	90000	1507500		-		-	-	0.013	-	-	2.087%
2014-04-04T00:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.767%
2014-05-04T12:46:00	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.012	-	-	0.970%
2014-10-03T21:04:00	Jocelyn Larouche	Manual testing	187203	187203		-		-	-	0.015	-	-	1.094%
2015-01-09T22:25:00	Jocelyn Larouche	Manual testing	280804	280804		-		-	-	0.022	-	-	1.345%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	373749	373749		-		-	-	0.029	-	-	1.541%
2015-02-22T09:50:00	Jocelyn Larouche	Manual testing	411123	411123		-		-	-	0.032	-	-	1.610%
2015-03-06T12:09:00	Jocelyn Larouche	Manual testing	452235	452235		-		-	-	0.036	-	-	1.681%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	497458	497458		-		-	-	0.039	-	-	1.754%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	601923	601923		-		-	-	0.047	-	-	1.904%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	728326	728326		-		-	-	0.057	-	-	2.062%
2015-05-07T16:18:00	Jocelyn Larouche	Manual testing	801158	801158		-		-	-	0.063	-	-	2.144%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	881273	881273		-		-	-	0.069	-	-	2.227%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	969400	969400		-		-	-	0.076	-	-	2.312%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1066340	1066340		-		-	-	0.084	-	-	2.399%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1172974	1172974		-		-	-	0.092	-	-	2.488%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1290271	1290271		-		-	-	0.101	-	-	2.578%
2015-07-21T01:19:00	Jocelyn Larouche	Manual testing	1419298	1419298		-		-	-	0.112	-	-	2.671%
2015-07-24T22:03:00	Jocelyn Larouche	Manual testing	1561227	1561227		-		-	-	0.123	-	-	2.764%
2015-08-31T03:59:00	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	7.963%
2018-10-03T11:47:44	Jocelyn Larouche	low 4M	1725233	17252330	12	-		-	-	0.202	-	-	5.309%
2018-10-07T10:38:15	Jocelyn Larouche	low 4M	1725233	69009320	12	-		-	-	0.424	-	-	6.827%
2018-10-12T11:50:58	Jocelyn Larouche	low 4M	1725233	172523300	12	-		-	-	0.868	-	-	7.850%
2018-10-17T22:59:49	Jocelyn Larouche	low 4M	1725233	189775630	12	-		-	-	0.942	-	-	7.957%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.067	-	-
2010-04-22T12:45:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.089	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.178	-	-
2010-10-27T20:37:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.925	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.569	-	-
2015-05-04T01:58:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.138	-	-
2015-05-04T01:58:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.166	-	-
2015-09-02T13:37:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.331	-	-
2018-04-09T13:44:25	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.663	-	-
2019-07-24T10:13:52	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.33	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.431 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	17.431 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.194	0.028%
25	50000	0.741	47.686%
30	250000	0.046	95.542%
35	1000000	0.002	99.791%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	17.22
50000	5000000	23780918273974220957487863	3	0.206

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-07T19:07:00	Team_Bundu	bundu4	50000	5000000						3	0.206
2009-06-28T21:23:00	James Hintz	10_060902	50000	5000000						3	0.206
2010-07-28T22:22:00	Lupo	yorick	50000	5000000						3	0.206
2011-12-09T10:45:00	S36049	Wolle5	50000	5000000						3	0.206
2013-04-30T18:02:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-01-27T03:00:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-11-03T20:02:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-07-05T10:01:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-11-22T20:35:22	mikr	MSI	50000	5000000						12	0.824
2016-09-20T20:55:21	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-11-22T01:40:40	Bruce	DESK3	50000	5000000						3	0.206
2017-01-16T02:35:18	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-05-09T23:42:39	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-12-02T05:12:07	Bruce	DESK3	50000	5000000						3	0.206
2018-02-02T08:18:07	Bruce	DESK3	50000	5000000						3	0.206
2019-07-12T14:16:39	storm5510	7700_Kaby_Lake	50000	5000000						3	0.206
2019-10-03T15:06:16	nordi	nordiputer	50000	5000000						50	3.431
2019-11-16T15:06:46	mnd9	dlounge	50000	5000000						3	0.206
2019-11-17T22:02:21	Nesowa	entropy_generator_2	50000	5000000						3	0.206
2020-02-07T09:44:07	J.R. Allen	lapacer-kubuntu	50000	5000000						3	0.206
2020-02-15T03:36:17	mnd9	75201b	50000	5000000						3	0.206
2020-02-22T13:00:05	mnd9	office2	50000	5000000						3	0.206
2020-02-29T04:26:29	Sergey Nosov	TS140-02	50000	5000000						3	0.206
2020-03-06T18:02:38	kracker	O0	50000	5000000						3	0.206
2020-03-13T14:55:05	mnd9	office2	50000	5000000						3	0.206
2020-03-21T17:23:54	mnd9	libproj	50000	5000000	23780918273974220957487863	84.298	3	2	1750146661672615	3	0.206
2020-05-18T10:37:58	TJAOI	Manual testing	50000	5000000						120	8.235

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	92A8D6AD08D9564F	0.094
2015-06-28T05:06:00	MadPoo	Manual testing	92A8D6AD08D9564F	0.094

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 = 1725233, B2 = 189775630 (P-1 stage 2)

B1 = 1725233, B2 = 172523300 (P-1 stage 2)

B1 = 3642200, B2 = 123456789 (P-1 stage 2)

B1 = 1725233, B2 = 69009320 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 1725233, B2 = 17252330 (P-1 stage 2)

B1 = 1725233 (P-1 stage 1)

B1 = 1561227 (P-1 stage 1)

B1 = 1419298 (P-1 stage 1)

B1 = 1290271 (P-1 stage 1)

B1 = 1172974 (P-1 stage 1)

B1 = 1066340 (P-1 stage 1)

B1 = 969400 (P-1 stage 1)

B1 = 881273 (P-1 stage 1)

B1 = 801158 (P-1 stage 1)

B1 = 728326 (P-1 stage 1)

B1 = 601923 (P-1 stage 1)

B1 = 497458 (P-1 stage 1)

B1 = 452235 (P-1 stage 1)

B1 = 411123 (P-1 stage 1)

B1 = 373749 (P-1 stage 1)

B1 = 280804 (P-1 stage 1)

B1 = 187203 (P-1 stage 1)

B1 = 90000, B2 = 1507500 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10³

10⁴

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10⁸

10⁹

10³

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10⁸

10⁹

10¹⁰

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