M3227221 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	2⁶⁹	36.9937	68.1159%	3750000	3250412550	22.2926	11.8159%	59.2863	71.8833%	3.7674%
PrimeNet	2⁶⁰	0.0476	63.3333%	13000	240000	0.0031	2.6615%	0.0507	64.3092%	0.9759%
GPU72	2⁶⁴	1.1029	65.6250%	16000	280000	0.0037	1.6526%	1.1067	66.1931%	0.5681%
Difference	+5	+35.8908	+2.4909%	+3734000	+3250132550	+22.2889	+10.1633%	+58.1797	+5.6903%	+5.6903%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3227221	96816631	8	26.529	15 3 × 5	-	3	5	2.779e-12	3.837e-7	7.535e-7
3227221	21163650598177	14	44.267	3278928 2⁴ × 3 × 68311	2008-09-30	16	68311	1.252e-6	0.0005	0.0009
3227221	79139049343793	14	46.169	12261176 2³ × 1532647	2014-02-05	8	1532647	5.618e-6	0.0103	0.0192
3227221	9365027980979129	16	53.056	1450943084 2² × 229 × 1583999	2014-09-02	229	1583999	0.0007	0.0107	0.0199
3227221	8409546581991047038795553	25	82.798	1302908381854085456 2⁴ × 47 × 1399 × 6301 × 196548097	2021-11-07	6301	196548097	322,947	1.3223	2.4683

exponent	prime factors	composite factor	digits	bits*
3227221	96816631 21163650598177	2048993350576631881687	22	70.795
3227221	96816631 79139049343793	7661976138008799021383	22	72.698
3227221	96816631 9365027980979129	906690458339131351094399	24	79.585
3227221	21163650598177 79139049343793	1674871188983923843772065361	28	90.436
3227221	21163650598177 9365027980979129	198198180031593286039002447833	30	97.323
3227221	79139049343793 9365027980979129	741139411492709422573078696297	30	99.226
3227221	96816631 8409546581991047038795553	814183968305938446458711739241943	33	109.327
3227221	96816631 21163650598177 79139049343793	162155385876387819714581700163818791	36	116.965
3227221	96816631 21163650598177 9365027980979129	19188880060990335516515551599944310623	38	123.852
3227221	96816631 79139049343793 9365027980979129	71754620922046807355480830673347715407	38	125.754
3227221	21163650598177 8409546581991047038795553	177976705550352168438264049774057506881	39	127.065
3227221	79139049343793 8409546581991047038795553	665523521911115237226994204457736552529	39	128.968
3227221	9365027980979129 8409546581991047038795553	78755639047693550563094811240621791013337	41	135.855
3227221	21163650598177 79139049343793 9365027980979129	15685215549370229519513181217382499364850569	44	143.492
3227221	96816631 21163650598177 8409546581991047038795553	17231105027864097811737256787540559016477737911	47	153.594
3227221	96816631 79139049343793 8409546581991047038795553	64433745242688858721083361132123234901412309799	47	155.497
3227221	96816631 9365027980979129 8409546581991047038795553	7624855644849737885946992557897932151097364407647	49	162.383
3227221	96816631 21163650598177 79139049343793 9365027980979129	15185897259988397937760149655594522268644719090130 39	52	170.021
3227221	21163650598177 79139049343793 8409546581991047038795553	14084907282595037756564255153903688429845848632139 633	53	173.234
3227221	21163650598177 9365027980979129 8409546581991047038795553	16667568274415315100068264970929502708608306830348 86649	55	180.121
3227221	79139049343793 9365027980979129 8409546581991047038795553	62326464046973706501204466871553731503193238943611 67241	55	182.024
3227221	96816631 21163650598177 79139049343793 8409546581991047038795553	13636532710482164929083493190253416122513549138997 17588636423	61	199.763
3227221	96816631 21163650598177 9365027980979129 8409546581991047038795553	16136978072913743027920372845007073907528309659286 6580823059519	63	206.650
3227221	96816631 79139049343793 9365027980979129 8409546581991047038795553	60342382711706200090294139246549420196177351364984 8109501185071	63	208.553
3227221	21163650598177 79139049343793 9365027980979129 8409546581991047038795553	13190555081099923678208067490771425095529520407545 8926237269586719657	69	226.291
3227221	96816631 21163650598177 79139049343793 9365027980979129 8409546581991047038795553	12770651039720263848812332114771129688180213269043 403017169948024959532215567	77	252.819

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-12-27T22:05:56	Jocelyn Larouche	Manual testing	322722	9681663	6	-	skipped known factor: 96816631 skipped known factor: 21163650598177 skipped known factor: 79139049343793 skipped known factor: 9365027980979129	-	-	0.103	-	-	3.868%
2021-09-13T11:19:25	Jocelyn Larouche	Manual testing	3227221	3227221		-	skipped known factor: 96816631 skipped known factor: 21163650598177 skipped known factor: 79139049343793 skipped known factor: 9365027980979129	-	-	0.398	-	-	3.464%
2021-11-07T02:34:41	Jocelyn Larouche	Manual testing	3227221	129088840	12		8409546581991047038795553	25	82.798	1.245	0.549	2.489	7.795%
2021-12-20T22:06:07	Jocelyn Larouche	Manual testing	3750000	116735850		-	skipped known factor: 96816631 skipped known factor: 21163650598177 skipped known factor: 79139049343793 skipped known factor: 9365027980979129	-	-	1.222	-	-	7.761%
2022-03-20T13:02:21	Jocelyn Larouche	Manual testing	3750000	1042528410		-	skipped known factor: 96816631 skipped known factor: 21163650598177 skipped known factor: 79139049343793 skipped known factor: 9365027980979129 skipped known factor: 8409546581991047038795553	-	-	7.447	-	-	10.432%
2022-07-21T21:50:43	Jocelyn Larouche	Manual testing	3750000	3250412550		-	skipped known factor: 96816631 skipped known factor: 21163650598177 skipped known factor: 79139049343793 skipped known factor: 9365027980979129 skipped known factor: 8409546581991047038795553	-	-	22.29	-	-	11.816%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T14:46:00	markr	Manual testing	?	?	21163650598177	44.267	14	5.26257e-7	0.605	1.15942e-6
2014-02-05T16:53:00	TJAOI	Manual testing	?	?	79139049343793	46.169	14	2.71365e-6	0.605	5.97852e-6
2014-09-02T11:40:00	TJAOI	Manual testing	?	?	9365027980979129	53.056	16	0.000	0.604	0.001
2021-02-01T19:24:58	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.316	-	-
2021-02-03T11:50:57	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.631	-	-
2021-02-04T01:07:14	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.262	-	-
2021-08-31T10:59:33	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	18.52	-	-

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.353

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-09-11T23:28:39	ATH	ec2-ECMCF	50000	5000000						3	0.353

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 = 3750000, B2 = 3250412550 (P-1 stage 2)

B1 = 3750000, B2 = 1042528410 (P-1 stage 2)

B1 = 3227221, B2 = 129088840 (P-1 stage 2)

B1 = 3750000, B2 = 116735850 (P-1 stage 2)

B1 = 3750000 (P-1 stage 1)

B1 = 3227221 (P-1 stage 1)

B1 = 322722, B2 = 9681663 (P-1 stage 2)

B1 = 322722 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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

Total ECM effort:	0.353 GHz-days
Estimated T-Level:	0.150

Total ECM effort:	0.353 GHz-days
Estimated T-Level:	0.150

Old Calculation Method

New Calculation Method