M4027 Mersenne number exponent details

is 2 ⁴⁰²⁷ - 1

has 1213 decimal digits

takes 0.000 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	7,378.6733	82.0896%	-	-	-	-	7,378.6733	82.0896%	12.0896%
PrimeNet	2⁴⁰	0.0000	70.0000%	500	10000	0.0000	2.3913%	0.0000	70.7174%	0.7174%
GPU72	2⁴⁴	0.0006	72.7273%	500	10000	0.0000	0.9515%	0.0006	72.9868%	0.2595%
Difference	+23	+7,378.6728	+9.3623%	-500	-10000	0.0000	-0.9515%	+7,378.6728	+9.1028%	+9.1028%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4027	82185762602338638075357407556967313	35	115.984	10204341023384484489118128576728 2³ × 23² × 47 × 246612745297 × 208029980948981	-	246612745297	208029980948981	4.723e+13	833.50	1,525.4
4027	1322603807888784213814883095222492416081030114751	49	159.856	164217011160762877305051290690649666759502125 3² × 5³ × 7 × 744654271 × 28003537494236854251274464137329	2020-10-01	744654271	28003537494236854251274464137329	3.659e+13	1.099e+20	2.053e+20
4027	55073558028420981931736977815277884416973711443146 602259410542519	65	215.065	68380379970723841484649835876928090907590900724045 94271096417 1483 × 2671 × 77213 × 599779 × 146988074533 × 11900314160518171 × 21310530479922829	2021-04-19	11900314160518171	21310530479922829	4.250e+13	894,443	1,745,161

exponent	prime factors	composite factor	digits	bits*
4027	82185762602338638075357407556967313 1322603807888784213814883095222492416081030114751	10869920257209671822295902713440857823938841706272 9385726327318622077143941946134063	84	275.840
4027	82185762602338638075357407556967313 55073558028420981931736977815277884416973711443146 602259410542519	45262623657899279936512956106707774992563682936814 52927495295260586658862991784280198707063679681447	100	331.049
4027	1322603807888784213814883095222492416081030114751 55073558028420981931736977815277884416973711443146 602259410542519	72840497562373513875872026471162378950740724921403 40166877746393517035122026733705978765763951882803 3933734597769	113	374.921
4027	82185762602338638075357407556967313 1322603807888784213814883095222492416081030114751 55073558028420981931736977815277884416973711443146 602259410542519	59864518404974558649575693667435736028017422606417 81285018713441936898736534661950676107855943267551 153043402912403879214535810705204803957535724697	148	490.905

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-02-11T00:00:00	ANONYMOUS	v4_computers	1000000	100000000		-		-	-	0.000	-	-	3.745%
2001-06-09T00:00:00	ANONYMOUS	v4_computers	43000000	4290000000		-		-	-	0.020	-	-	9.676%
2001-06-23T00:00:00	ANONYMOUS	v4_computers	3000000000	4290000000		-		-	-	0.221	-	-	10.761%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	1073741824	4290000000		-		-	-	0.090	-	-	10.798%
2002-08-03T00:00:00	ANONYMOUS	v4_computers	2147483648	4290000000		-		-	-	0.163	-	-	10.794%
2002-09-22T00:00:00	ANONYMOUS	v4_computers	3221225472	4290000000		-		-	-	0.236	-	-	10.752%
2003-01-01T00:00:00	ANONYMOUS	v4_computers	4290000000	2147483647		-		-	-	0.309	-	-	10.704%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-09-22T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.149	-	-
1999-12-23T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.298	-	-
2000-02-09T00:00:00	ANONYMOUS	v4_computers	2⁵⁴	2⁵⁵		-	-	0.596	-	-
2000-08-24T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁶		-	-	2.384	-	-
2003-01-25T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁷		-	-	4.768	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	115.065 GHz-days
Estimated T-Level:	43.408

Digits	B1	Curves	Complete	FacMiss
20	11000	8277 / 100	82.770	0.000%
25	50000	8277 / 280	29.561	0.000%
30	250000	8277 / 640	12.933	0.000%
35	1000000	8185 / 1580	5.180	0.562%
40	3000000	8185 / 4700	1.741	17.523%
45	11000000	6611 / 9700	0.682	50.582%
50	44000000	202 / 17100	0.012	98.826%
55	110000000	202 / 46500	0.004	99.567%

New Calculation Method

Total ECM effort:	115.065 GHz-days
Estimated T-Level:	43.408

Digits	B1	Complete	FacMiss
20	11000	1,993.917	0.000%
25	50000	640.148	0.000%
30	250000	150.806	0.000%
35	1000000	30.172	0.000%
40	3000000	5.149	0.581%
45	11000000	0.777	45.992%
50	44000000	0.106	89.912%
55	110000000	0.013	98.663%
60	260000000	0.002	99.840%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		1,574	4.896
11000000	11000000		92	0.711
11000000	1100000000		6,409	73.10
110000000	11000000000		200	22.81
110000000	900514153782	1322603807888784213814883095222492416081030114751	1	3.114
260000000	3039198402256	55073558028420981931736977815277884416973711443146 602259410542519	1	10.43

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-12T10:30:00	Carsten Kossendey	durandal	3000000	300000000						1	0.003
2009-10-13T12:31:00	Carsten Kossendey	durandal	3000000	300000000						1	0.003
2010-05-29T04:13:00	James Hintz	18_051310	3000000	300000000						100	0.311
2010-05-29T04:30:00	James Hintz	17_051310	3000000	300000000						100	0.311
2010-05-29T04:33:00	James Hintz	17_051310	3000000	300000000						100	0.311
2010-05-29T04:34:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-05-29T09:40:00	James Hintz	13_052010	3000000	300000000						100	0.311
2010-05-30T09:59:00	James Hintz	18_051310	3000000	300000000						100	0.311
2010-05-31T13:45:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-05-31T19:12:00	James Hintz	13_052010	3000000	300000000						100	0.311
2010-06-01T08:56:00	James Hintz	18_051310	3000000	300000000						100	0.311
2010-06-01T13:16:00	James Hintz	17_051310	3000000	300000000						100	0.311
2010-06-01T13:33:00	James Hintz	17_051310	3000000	300000000						100	0.311
2010-06-02T03:22:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-06T22:37:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-16T00:06:00	James Hintz	13_052010	3000000	300000000						272	0.846
2010-12-30T03:30:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-01T17:40:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-05T06:31:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-06T14:48:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-13T16:36:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-23T13:04:00	James Hintz	OMFG	11000000	1100000000						11	0.125
2016-09-30T12:36:20	kkmrkkblmbrbk	kel1	11000000	11000000						92	0.711
2018-10-07T00:37:03	eteo	stephanie	110000000	11000000000						200	22.81
2020-02-22T18:02:42	James Hintz	work_5_9_2019	11000000	1100000000						6383	72.80
2020-10-01T12:04:10	Ryan Propper	Manual testing	110000000	900514153782	1322603807888784213814883095222492416081030114751	159.856	1	2	6082699471423120831	1	3.114
2021-04-19T16:57:52	Ryan Propper	Manual testing	260000000	3039198402256	55073558028420981931736977815277884416973711443146 602259410542519	215.065	1	2	2267136871149356697	1	10.43

Lucas-Lehmer results:
Exponent "4027" not found

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:33:06

Oliver Kruse

Oliver-PC

82185762602338638075357407556967313

C88D2D68CF5533__

2017-09-21T19:21:09

Oliver Kruse

Manual testing

82185762602338638075357407556967313

C88D2D68CF5533__

2017-10-12T13:52:41

kkmrkkblmbrbk

Manual testing

82185762602338638075357407556967313

C88D2D68CF5533__

2020-04-17T12:32:13

Oliver Kruse

IOS-1

82185762602338638075357407556967313

872B4531B1C520__

2020-10-01T15:22:05

mnd9

82185762602338638075357407556967313

1322603807888784213814883095222492416081030114751

872B4531B1C5209A

2020-10-02T18:09:13

Lord Julius

BlackboxNouveau

82185762602338638075357407556967313

1322603807888784213814883095222492416081030114751

872B4531B1C5209A

2021-04-19T20:28:39

mnd9

50871

82185762602338638075357407556967313

1322603807888784213814883095222492416081030114751

55073558028420981931736977815277884416973711443146
602259410542519

872B4531B1C5209A

2021-04-20T06:59:12

XZT

800G3Mini2

82185762602338638075357407556967313

1322603807888784213814883095222492416081030114751

55073558028420981931736977815277884416973711443146
602259410542519

872B4531B1C5209A

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 = 4290000000 (P-1 stage 1)

B1 = 3221225472, B2 = 4290000000 (P-1 stage 2)

B1 = 3221225472 (P-1 stage 1)

B1 = 3000000000, B2 = 4290000000 (P-1 stage 2)

B1 = 3000000000 (P-1 stage 1)

B1 = 2147483648, B2 = 4290000000 (P-1 stage 2)

B1 = 2147483648 (P-1 stage 1)

B1 = 1073741824, B2 = 4290000000 (P-1 stage 2)

B1 = 1073741824 (P-1 stage 1)

B1 = 43000000, B2 = 4290000000 (P-1 stage 2)

B1 = 43000000 (P-1 stage 1)

B1 = 1000000, B2 = 100000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

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TF factor-bounds graph:

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Last modified: 2021-04-20T06:59:12+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