M202109 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	147.0193	73.1343%	30000000	10264076402580	3,739.1646	23.1623%	3,886.1839	79.3570%	6.2227%
PrimeNet	2⁴⁰	0.0000	55.0000%	2200	50000	0.0000	12.6646%	0.0000	60.6991%	5.6991%
GPU72	2⁴⁴	0.0000	59.0909%	3600	80000	0.0001	8.8808%	0.0001	62.7240%	3.6331%
Difference	+23	+147.0193	+14.0434%	+29996400	+10264076322580	+3,739.1645	+14.2815%	+3,886.1838	+16.6331%	+16.6331%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
202109	1982394615079	13	40.850	4904271 3² × 544919	-	9	544919	1.109e-6	0.0002	0.0004
202109	45246143446873	14	45.363	111935004 2² × 3 × 17 × 19 × 28879	2008-07-21	19	28879	3.144e-5	1.064e-5	1.965e-5

exponent	prime factors	composite factor	digits	bits*
202109	1982394615079 45246143446873	89695711122173019121197967	26	86.213

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-05-04T18:17:53	Oliver Kruse	Ollaptop	30000000	3000000000		-	skipped known factor: 1982394615079 skipped known factor: 45246143446873	-	-	1.282	-	-	12.368%
2022-02-04T13:45:19	Oliver Kruse	Threadripper-PC	30000000	10264076402580		-	skipped known factor: 1982394615079 skipped known factor: 45246143446873	-	-	3,739	-	-	23.162%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-21T09:13:00	J Feitsma	Manual testing	?	?	45246143446873	45.363	14	8.25254e-6	0.002	1.71161e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.071 GHz-days
Estimated T-Level:	28.367

Digits	B1	Curves	Complete	FacMiss
20	11000	712 / 100	7.120	0.078%
25	50000	712 / 280	2.543	7.828%
30	250000	431 / 640	0.673	50.968%

New Calculation Method

Total ECM effort:	12.071 GHz-days
Estimated T-Level:	28.367

Digits	B1	Complete	FacMiss
20	11000	50.444	0.000%
25	50000	7.126	0.080%
30	250000	0.740	47.691%
35	1000000	0.060	94.143%
40	3000000	0.004	99.599%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	1.372
250000	25000000		381	9.300
250000	31250000		7	0.185
250000	33250000		7	0.189
250000	35928186		7	0.196
250000	36000000		7	0.196
250000	38500000		21	0.604
250000	38500000	45246143446873	1	0.029

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-07-28T13:20:00	TJAOI	Manual testing	50000	5000000						50	0.244
2014-12-12T13:36:00	TJAOI	Manual testing	50000	5000000						50	0.244
2015-06-19T10:47:00	TJAOI	Manual testing	50000	5000000						90	0.439
2016-02-26T13:28:48	TJAOI	Manual testing	50000	5000000						91	0.444
2018-01-26T15:17:01	TJAOI	Manual testing	250000	25000000						44	1.074
2019-06-10T21:42:16	happy5214	Cosmic	250000	25000000						3	0.073
2019-09-03T13:48:44	storm5510	M520_Arrandale	250000	25000000						3	0.073
2019-11-20T01:28:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-20T04:12:07	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-20T07:00:57	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-20T10:12:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-20T14:25:03	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-20T19:05:07	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-21T00:22:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-21T06:03:26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-21T11:52:04	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-21T18:35:46	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-22T01:28:36	ATH	ec2-ECMCF	250000	25000000						3	0.073
2019-11-22T11:01:04	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-22T20:38:06	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-23T07:16:55	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-23T20:26:24	kracker	O0	250000	25000000						3	0.073
2019-11-24T07:44:35	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-24T20:54:28	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-25T10:23:19	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-26T00:39:15	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-26T15:35:25	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-27T08:16:54	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-28T01:14:13	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-28T19:54:26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-29T15:44:30	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-30T13:52:09	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-01T13:18:56	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-02T12:30:02	ATH	ec2-ECMCF	250000	25000000						3	0.073
2019-12-03T16:28:38	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-04T23:46:23	Ducho_YYZ	oracle	250000	25000000						3	0.073
2019-12-07T00:30:35	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-07T04:53:04	alan145	Bear1	250000	25000000						3	0.073
2019-12-08T02:41:37	Ducho_YYZ	oracleDE	250000	25000000						3	0.073
2019-12-09T03:07:09	kracker	O0	250000	25000000						3	0.073
2019-12-10T01:19:49	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-11T01:24:57	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-12T06:48:11	Chang Chia-Tche	exbpc13	250000	25000000						3	0.073
2019-12-13T02:31:54	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-14T05:08:23	kracker	O0	250000	25000000						3	0.073
2019-12-15T10:28:03	Ducho_YYZ	oracleKO	250000	25000000						3	0.073
2019-12-16T07:46:54	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-17T15:51:05	Ducho_YYZ	oracleKO	250000	25000000						3	0.073
2019-12-18T15:19:30	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-19T20:31:27	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-21T02:51:33	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-22T15:57:07	Ducho_YYZ	oracleSW2	250000	25000000						3	0.073
2019-12-24T02:10:22	Ducho_YYZ	oracleSP2	250000	25000000						3	0.073
2019-12-25T08:28:04	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-27T08:11:48	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-29T05:43:50	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-31T03:44:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-02T04:10:33	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-04T07:05:54	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-06T09:30:22	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-08T14:48:47	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-10T17:45:00	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-13T00:03:07	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-15T04:53:48	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-17T10:47:14	kracker	O0	250000	25000000						3	0.073
2020-01-19T17:23:45	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-22T04:01:43	kracker	O0	250000	25000000						3	0.073
2020-01-24T12:59:08	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						3	0.073
2020-01-26T20:50:51	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-29T10:29:01	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-01T05:26:50	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-04T06:09:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-07T10:30:26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-10T19:50:28	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-14T12:38:19	kracker	O0	250000	25000000						3	0.073
2020-02-18T06:41:35	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-21T11:24:30	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-25T08:31:04	kracker	O0	250000	25000000						3	0.073
2020-02-28T08:59:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-03-03T16:30:54	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-03-08T14:39:29	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-03-14T12:56:37	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-03-19T22:15:11	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-04-08T02:01:49	Oliver Kruse	Melissa	250000	25000000						3	0.073
2020-04-18T23:09:04	Oliver Kruse	Melissa	250000	25000000						3	0.073
2020-05-01T07:57:04	Greg	azure3	250000	25000000						3	0.073
2020-05-06T01:32:35	Greg Hogan	azure	250000	25000000						3	0.073
2020-05-20T01:46:50	kracker	O0	250000	25000000						3	0.073
2020-06-06T13:46:51	Chang Chia-Tche	exbpc13	250000	25000000						3	0.073
2020-06-20T18:09:22	_p95holder_	TFL1_PRPt8pE_n	250000	25000000						3	0.073
2020-06-29T20:40:13	-Anonymous-	aws-nano	250000	25000000						3	0.073
2020-07-14T18:46:27	-Anonymous-	aws-nano	250000	25000000						3	0.073
2020-07-24T18:27:08	Ahmed Azhad	c5.4xlarge.azf	250000	25000000						3	0.073
2020-08-10T20:31:52	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						3	0.073
2020-09-23T17:33:40	nordi	sweet16	250000	25000000						7	0.171
2020-10-27T11:30:53	nordi	sweet16	250000	25000000						7	0.171
2020-11-10T18:41:10	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.171
2021-01-09T11:26:34	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.171
2021-02-01T21:15:47	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.171
2021-03-14T12:27:54	Deufo	Ryzen2600	250000	38500000						7	0.201
2021-05-06T02:15:43	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.171
2021-07-11T19:04:22	seatsea	Manual testing	250000	38500000	45246143446873	45.363	1	2		1	0.029
2021-07-12T13:36:54	rushyn	linux	250000	25000000						7	0.171
2021-07-14T09:07:01	seatsea	Manual testing	250000	38500000						7	0.201
2021-09-20T21:38:00	jocosum	ryzen3	250000	25000000						7	0.171
2021-10-26T00:39:44	Dylan Delgado	colab	250000	38500000						7	0.201
2022-01-05T01:05:39	JackBlock	school2	250000	25000000						7	0.171
2022-03-08T01:14:35	tim s	voyager1	250000	33250000						7	0.189
2022-05-09T20:35:53	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.171
2022-06-02T12:49:51	Eric	miniPCWindows	250000	31250000						7	0.185
2022-06-28T18:56:05	debrouxl	o9020	250000	36000000						7	0.196
2022-07-24T10:15:37	debrouxl	dl380g9-1	250000	35928186						7	0.196

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