M1884121 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	15.7707	68.6567%	500000	15000000	0.1015	5.0864%	15.8722	70.2510%	1.5942%
PrimeNet	2⁵⁷	0.0102	63.1579%	9000	160000	0.0014	3.0333%	0.0115	64.2754%	1.1175%
GPU72	2⁶¹	0.1630	65.5738%	10000	150000	0.0014	1.6922%	0.1644	66.1563%	0.5826%
Difference	+6	+15.6077	+3.0829%	+490000	+14850000	+0.1001	+3.3942%	+15.7078	+4.0946%	+4.0946%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.7707

68.6567%

500000

15000000

0.1015

5.0864%

15.8722

70.2510%

1.5942%

PrimeNet

2⁵⁷

0.0102

63.1579%

9000

160000

0.0014

3.0333%

0.0115

64.2754%

1.1175%

GPU72

2⁶¹

0.1630

65.5738%

10000

150000

0.0014

1.6922%

0.1644

66.1563%

0.5826%

Difference

+15.6077

+3.0829%

+490000

+14850000

+0.1001

+3.3942%

+15.7078

+4.0946%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1884121	1141777327	10	30.089	303 3 × 101	-	3	101	8.090e-11	6.560e-7	8.047e-7
1884121	31845413143	11	34.890	8451 3³ × 313	2008-07-15	27	313	2.222e-9	3.350e-6	4.322e-6
1884121	32366150272223	14	44.880	8589191 13 × 29 × 22783	2008-08-26	29	22783	1.408e-6	9.980e-5	0.0002
1884121	105199760924377557170399	24	76.477	27917464144918919 157 × 177818242961267	2021-10-07	157	177818242961267	15,083	762,085	1,423,362
1884121	37147423077558317295956911	26	84.941	9858024797122455855 3 × 5 × 11 × 211 × 317 × 58543 × 15257707	2020-11-15	58543	15257707	3,490,445	0.0697	0.1221

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1884121

1141777327

30.089

303
3 × 101

101

8.090e-11

6.560e-7

8.047e-7

1884121

31845413143

34.890

8451
3³ × 313

2008-07-15

313

2.222e-9

3.350e-6

4.322e-6

1884121

32366150272223

44.880

8589191
13 × 29 × 22783

2008-08-26

22783

1.408e-6

9.980e-5

0.0002

1884121

105199760924377557170399

76.477

27917464144918919
157 × 177818242961267

2021-10-07

157

177818242961267

15,083

762,085

1,423,362

1884121

37147423077558317295956911

84.941

9858024797122455855
3 × 5 × 11 × 211 × 317 × 58543 × 15257707

2020-11-15

58543

15257707

3,490,445

0.0697

0.1221

exponent	prime factors	composite factor	digits	bits*
1884121	1141777327 31845413143	36360370695625208761	20	64.979
1884121	1141777327 32366150272223	36954936543099099287921	23	74.968
1884121	31845413143 32366150272223	1030713427267363352026889	25	79.770
1884121	1141777327 105199760924377557170399	120114701829274856364807853743473	33	106.566
1884121	1141777327 31845413143 32366150272223	1176845221888339042415021354545703	34	109.859
1884121	31845413143 105199760924377557170399	3350129849181630888208458205154057	34	111.368
1884121	1141777327 37147423077558317295956911	42414085426432649208795549748756897	35	115.030
1884121	31845413143 37147423077558317295956911	1182975035102657145965630434321081273	37	119.832
1884121	32366150272223 105199760924377557170399	3404911270680337190127541339447526977	37	121.357
1884121	32366150272223 37147423077558317295956911	1202319077554097083790693584219928183153	40	129.821
1884121	1141777327 31845413143 105199760924377557170399	3825102304301515653039289228272016824665639	43	141.456
1884121	1141777327 31845413143 37147423077558317295956911	1350694073487243046718086351168973235635697271	46	149.920
1884121	1141777327 32366150272223 105199760924377557170399	3887650489309568868402514939636397008559450479	46	151.446
1884121	31845413143 32366150272223 105199760924377557170399	108430806130072440506159294817518099952202858711	48	156.247
1884121	1141777327 32366150272223 37147423077558317295956911	1372780662570822666229033148066678981092398772031	49	159.910
1884121	105199760924377557170399 37147423077558317295956911	3907900026715840565147178619601715076360188677489	49	161.419
1884121	31845413143 32366150272223 37147423077558317295956911	38288347754420879565646125728003078366296657379879	50	164.711
1884121	1141777327 31845413143 32366150272223 105199760924377557170399	12380383598764932543748908667295076893754500778080 4245497	57	186.336
1884121	1141777327 105199760924377557170399 37147423077558317295956911	44619516466868410290319149658803960445021371173990 55491903	58	191.508
1884121	1141777327 31845413143 32366150272223 37147423077558317295956911	43716767354289124303452354461625283864841724352233 068203433	59	194.800
1884121	31845413143 105199760924377557170399 37147423077558317295956911	12444869087230668025963050974203305471806200111206 7988837927	60	196.309
1884121	32366150272223 105199760924377557170399 37147423077558317295956911	12648367951350917208030462144488245578257300399591 0239702088047	63	206.298
1884121	1141777327 31845413143 105199760924377557170399 37147423077558317295956911	14209269361283161971108458942090596076163357025000 8015737634126281129	69	226.398
1884121	1141777327 32366150272223 105199760924377557170399 37147423077558317295956911	14441619750405916288783324001908476819262189768481 0712418979366622310369	72	236.387
1884121	31845413143 32366150272223 105199760924377557170399 37147423077558317295956911	40279250299545048346171814432044994074684666918083 51465657155096477001721	73	241.189
1884121	1141777327 31845413143 32366150272223 105199760924377557170399 37147423077558317295956911	45989934740578494616777824964960356478324297361614 72332734558844479938141977779767	82	271.277

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:39:51	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1141777327 skipped known factor: 31845413143 skipped known factor: 32366150272223	-	-	0.101	-	-	5.086%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:39:51

alpertron

Manual testing

500000

15000000

skipped known factor: 1141777327
skipped known factor: 31845413143
skipped known factor: 32366150272223

0.101

-

-

5.086%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	32366150272223	44.880	14	1.64503e-7	0.218	3.50899e-7
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	31845413143	34.890	11	1.00727e-9	0.218	2.14862e-9

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T20:20:00

ANONYMOUS

Manual testing

32366150272223

44.880

1.64503e-7

0.218

3.50899e-7

2008-07-15T07:47:00

J Feitsma

Manual testing

31845413143

34.890

1.00727e-9

0.218

2.14862e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.802 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	19.802 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	8.789	0.015%
25	50000	0.796	45.091%
30	250000	0.049	95.192%
35	1000000	0.002	99.774%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		28	1.940
50000	5000000	37147423077558317295956911	5	0.346
50000	6600000		193	15.09
50000	6600000	105199760924377557170399	24	1.876
50000	6750000		7	0.553

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

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-02-26T03:18:35	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-20T19:22:19	ATH	ec2-ECMCF	50000	5000000						3	0.208
2020-07-17T00:28:00	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						3	0.208
2020-09-15T06:22:22	LaurV	3tits	50000	5000000						7	0.485
2020-11-15T22:00:17	MarkS	desktop-i7	50000	5000000	37147423077558317295956911	84.941	5	2	8584982327939917	5	0.346
2021-01-22T07:11:45	nordi	sweet16	50000	6750000						7	0.553
2021-05-11T19:37:47	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.485
2021-08-15T07:11:34	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2021-10-07T10:32:23	TJAOI	Manual testing	50000	6600000	105199760924377557170399	76.477	24	2		24	1.876
2021-10-20T13:19:03	TJAOI	Manual testing	50000	6600000						193	15.09