M304211 Mersenne number exponent details

is 2 ³⁰⁴²¹¹ - 1

has 91577 decimal digits

takes 0.002 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	97.6754	71.6418%	50000	50000	0.0005	0.4001%	97.6759	71.7552%	0.1135%
PrimeNet	2⁴⁰	0.0000	52.5000%	3200	90000	0.0001	15.5967%	0.0001	59.9085%	7.4085%
GPU72	2⁴⁴	0.0000	56.8182%	5500	150000	0.0001	11.4151%	0.0001	61.7474%	4.9292%
Difference	+23	+97.6753	+14.8236%	+44500	-100000	+0.0004	-11.0150%	+97.6757	+10.0078%	+10.0078%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
304211	608423	6	19.215	1 1	-	1	1	2.296e-13	1.031e-8	2.098e-8
304211	32686863529	11	34.928	53724 2² × 3 × 11² × 37	2008-07-21	121	121	1.225e-8	1.248e-6	2.539e-6
304211	6929021856487	13	42.656	11388513 3 × 83 × 45737	2008-07-21	83	45737	2.015e-6	2.650e-5	4.799e-5
304211	24151556304810129540958273	26	84.320	39695402705375758176 2⁵ × 3² × 11 × 43 × 291398011403099	2015-11-06	43	291398011403099	19,502,158	163,701	305,748
304211	116369922592922102619666191	27	86.589	191265145890388747645 5 × 13 × 2942540706005980733	2021-11-11	13	2942540706005980733	91,935,562	1.653e+9	3.087e+9

exponent	prime factors	composite factor	digits	bits*
304211	608423 32686863529	19887439568904767	17	54.143
304211	608423 6929021856487	4215776264989390001	19	61.871
304211	32686863529 6929021856487	226487991812448792362623	24	77.584
304211	608423 32686863529 6929021856487	137800503442505531595644173529	30	96.798
304211	608423 24151556304810129540958273	14694362341641493445698455333479	32	103.535
304211	608423 116369922592922102619666191	70802137413753444442165162926793	32	105.804
304211	32686863529 24151556304810129540958273	789438624948288230562114485434525417	36	119.248
304211	32686863529 116369922592922102619666191	3803767778675138589656762176752248039	37	121.517
304211	6929021856487 24151556304810129540958273	167346661504205793439933653887461366951	39	126.976
304211	6929021856487 116369922592922102619666191	806329737084057592259894956839047931017	39	129.245
304211	608423 32686863529 24151556304810129540958273	480312616506912370103293381571530257787391	42	138.463
304211	608423 32686863529 116369922592922102619666191	2314299803204863846134736213866133008632497	43	140.732
304211	608423 6929021856487 24151556304810129540958273	101817557832373401462104753499170907264428273	45	146.191
304211	608423 6929021856487 116369922592922102619666191	490589557625893572455542069324884059333156191	45	148.459
304211	32686863529 6929021856487 24151556304810129540958273	5470037486621732629702274803433770025787127830079	49	161.904
304211	32686863529 6929021856487 116369922592922102619666191	26356390075441040919775513154073304939442485178993	50	164.173
304211	24151556304810129540958273 116369922592922102619666191	28105147376893545452764876547057082723120375198481 43	52	170.909
304211	608423 32686863529 6929021856487 24151556304810129540958273	33280966177228544317613471427295846603994816757601 55417	55	181.119
304211	608423 32686863529 6929021856487 116369922592922102619666191	16035833918870064439532577039740742411170415160058 458039	56	183.387
304211	608423 24151556304810129540958273 116369922592922102619666191	17099818082491701605007564483390111441649068039385 66708489	58	190.124
304211	32686863529 24151556304810129540958273 116369922592922102619666191	91866911677095164817548403541818760954349939715203 879045076647	62	205.837
304211	6929021856487 24151556304810129540958273 116369922592922102619666191	19474118045428365260008440185919683354651787555535 778920179453641	65	213.565
304211	608423 32686863529 24151556304810129540958273 116369922592922102619666191	55893942003313271463787252328123995996128453371343 489700242668797681	68	225.052
304211	608423 6929021856487 24151556304810129540958273 116369922592922102619666191	11848501323553662276590115203237811505687304539901 745217952343722618143	71	232.780
304211	32686863529 6929021856487 24151556304810129540958273 116369922592922102619666191	63654783889855319759946048574531607716839588714369 8514040620785353149159089	75	248.493
304211	608423 32686863529 6929021856487 24151556304810129540958273 116369922592922102619666191	38729034578617443214305654711862244361902693084363 0481008136620086919070820406647	81	267.708

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-02-06T16:51:24	Lisander Viaene	Manual testing	50000	50000		-	skipped known factor: 608423 skipped known factor: 32686863529 skipped known factor: 6929021856487	-	-	0.001	-	-	0.400%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-04-24T07:58:14	nordi	sweet16	10000000	1010000000	2	7			-	-	0.694
2021-04-30T11:01:50	nordi	sweet16	10000000	1010000000	6	5			-	-	0.694

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-21T09:16:00	J Feitsma	Manual testing	?	?	32686863529	34.928	11	4.72893e-9	0.004	9.83237e-9
2008-07-21T09:16:00	J Feitsma	Manual testing	?	?	6929021856487	42.656	13	8.87945e-8	0.004	1.84602e-7

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.787 GHz-days
Estimated T-Level:	27.203

Digits	B1	Curves	Complete	FacMiss
20	11000	573 / 100	5.730	0.315%
25	50000	573 / 280	2.046	12.872%
30	250000	282 / 640	0.441	64.341%

New Calculation Method

Total ECM effort:	13.787 GHz-days
Estimated T-Level:	27.203

Digits	B1	Complete	FacMiss
20	11000	32.887	0.000%
25	50000	4.309	1.344%
30	250000	0.427	65.239%
35	1000000	0.033	96.711%
40	3000000	0.002	99.783%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		220	1.679
50000	5000000	24151556304810129540958273	71	0.542
250000	25000000		142	5.418
250000	35500000		51	2.219
250000	36750000	116369922592922102619666191	89	3.930

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-01-01T05:04:00	Richard B. Woods	Puttputt	50000	5000000						10	0.076
2014-09-19T12:42:00	TJAOI	Manual testing	50000	5000000						40	0.305
2015-02-20T13:24:00	TJAOI	Manual testing	50000	5000000						50	0.382
2015-11-06T13:40:27	TJAOI	Manual testing	50000	5000000						19	0.145
2015-11-06T13:40:27	TJAOI	Manual testing	50000	5000000	24151556304810129540958273	84.320	71	2		71	0.542
2016-04-10T11:45:43	Richard B. Woods	Puttputt	50000	5000000						10	0.076
2016-06-10T14:40:50	TJAOI	Manual testing	50000	5000000						91	0.694
2018-01-19T13:22:50	TJAOI	Manual testing	250000	25000000						42	1.602
2019-03-15T12:26:45	TJAOI	Manual testing	250000	25000000						100	3.815
2021-11-11T20:25:56	nordi	sweet16	250000	36750000	116369922592922102619666191	86.589	89	2	3447341434191616	89	3.930
2021-11-13T15:03:45	nordi	sweet16	250000	35500000						51	2.219

Lucas-Lehmer results:
No L-L results for M304211

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T15:22:48

Oliver Kruse

Ollaptop

CE1F2E284B5BDF__

2017-09-22T20:37:20

Oliver Kruse

Manual testing

CE1F2E284B5BDF__

2017-10-12T22:18:27

Oliver Kruse

GTX-0

CE1F2E284B5BDF__

2017-12-11T07:10:52

ATH

xps

608423

32686863529

6929021856487

24151556304810129540958273

CE1F2E284B5BDF__

2020-04-18T07:34:58

Oliver Kruse

AddPrpType5

608423

32686863529

6929021856487

24151556304810129540958273

0B991CBE8E4712__

2021-11-11T20:47:31

mikr

Nitron

608423

32686863529

6929021856487

24151556304810129540958273

116369922592922102619666191

0B991CBE8E471204

2022-05-12T18:24:17

Jorge Coveiro

Manual testing

608423

0B991CBE8E471204

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 = 50000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

TF factor-bounds graph:

2⁶⁷

2¹⁰

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-12T18:24:17+00:00

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