M1950419 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	15.2346	68.6567%	500000	15000000	0.1015	5.1076%	15.3361	70.2576%	1.6009%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4669%	0.0209	64.6863%	0.8932%
GPU72	2⁶²	0.3150	66.1290%	8000	90000	0.0010	1.1532%	0.3160	66.5196%	0.3906%
Difference	+5	+14.9196	+2.5277%	+492000	+14910000	+0.1005	+3.9545%	+15.0201	+3.7380%	+3.7380%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.2346

68.6567%

500000

15000000

0.1015

5.1076%

15.3361

70.2576%

1.6009%

PrimeNet

2⁵⁸

0.0197

63.7931%

8000

140000

0.0012

2.4669%

0.0209

64.6863%

0.8932%

GPU72

2⁶²

0.3150

66.1290%

8000

90000

0.0010

1.1532%

0.3160

66.5196%

0.3906%

Difference

+14.9196

+2.5277%

+492000

+14910000

+0.1005

+3.9545%

+15.0201

+3.7380%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1950419	3900839	7	21.895	1 1	-	1	1	1.433e-13	7.866e-8	1.601e-7
1950419	15603353	8	23.895	4 2²	2008-07-15	4	4	5.735e-13	3.146e-7	6.404e-7
1950419	205555492556292306847	21	67.478	52695213837717 3 × 11 × 1596824661749	2020-11-22	11	1596824661749	16.220	6,843.6	12,782
1950419	2200093016775877920311	22	70.898	564005225742745 5 × 359 × 10457 × 30047723	2021-09-01	10457	30047723	131.14	0.1296	0.2405

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1950419

3900839

21.895

1
1

1.433e-13

7.866e-8

1.601e-7

1950419

15603353

23.895

4
2²

2008-07-15

5.735e-13

3.146e-7

6.404e-7

1950419

205555492556292306847

67.478

52695213837717
3 × 11 × 1596824661749

2020-11-22

1596824661749

16.220

6,843.6

12,782

1950419

2200093016775877920311

70.898

564005225742745
5 × 359 × 10457 × 30047723

2021-09-01

10457

30047723

131.14

0.1296

0.2405

exponent	prime factors	composite factor	digits	bits*
1950419	3900839 15603353	60866167913167	14	45.791
1950419	3900839 205555492556292306847	801838882027794725948744633	27	89.373
1950419	15603353 205555492556292306847	3207354911444701234918057991	28	91.373
1950419	3900839 2200093016775877920311	8582208643466998850788040929	28	92.793
1950419	15603353 2200093016775877920311	34328827973588945075518402783	29	94.793
1950419	3900839 15603353 205555492556292306847	12511375125405036920516522415554449	35	113.269
1950419	3900839 15603353 2200093016775877920311	133911230983666726919440130793634937	36	116.689
1950419	205555492556292306847 2200093016775877920311	452241203733024659221692996685459025669417	42	138.376
1950419	3900839 205555492556292306847 2200093016775877920311	1764120124928728178653689687497509300233262940863	49	160.271
1950419	15603353 205555492556292306847 2200093016775877920311	7056479142991301515540781084911047144555974755201	49	162.271
1950419	3900839 15603353 205555492556292306847 2200093016775877920311	27526189043667045612580584946483324232322584008103 513639	56	184.167

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:19:13	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 3900839 skipped known factor: 15603353	-	-	0.101	-	-	5.108%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:19:13

alpertron

Manual testing

500000

15000000

skipped known factor: 3900839
skipped known factor: 15603353

0.101

-

-

5.108%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:48:00	J Feitsma	Manual testing	?	?	15603353	23.895	8	4.96071e-16	0.235	1.10011e-15

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:48:00

J Feitsma

Manual testing

15603353

23.895

4.96071e-16

0.235

1.10011e-15

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.074 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:	21.074 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	9.076	0.011%
25	50000	0.807	44.609%
30	250000	0.050	95.117%
35	1000000	0.002	99.770%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.252
50000	5000000	205555492556292306847	6	0.417
50000	6500000	2200093016775877920311	2	0.156
50000	6750000		14	1.111
50000	7500000		217	18.14

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-07-28T12:17:45	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-14T08:16:52	Oliver Kruse	ECM-HTC	50000	5000000						3	0.209
2020-11-22T06:42:57	MarkS	desktop-i7	50000	5000000	205555492556292306847	67.478	6	2	6293033908384361	6	0.417
2021-02-07T10:10:39	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.487
2021-05-28T18:37:28	happy5214	Focus	50000	6750000						7	0.556
2021-09-01T13:44:55	Team_Inspector	SpudBoy4	50000	6500000	2200093016775877920311	70.898	2	2	4873068625447823	2	0.156
2021-09-23T15:19:50	Ahmed Azhad	c5.4xlarge.azf	50000	6750000						7	0.556
2022-02-12T03:27:34	MarkS	desktop-i7	50000	5000000						7	0.487
2022-04-28T10:18:13	TJAOI	Manual testing	50000	7500000						217	18.14

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T05:28:34

Oliver Kruse

GTX-1

3900839

15603353

8A3552F3079736__

2017-11-11T12:22:26

kkmrkkblmbrbk

c4.xlarge

3900839

15603353

8A3552F3079736__

2020-11-22T07:59:32

SRJ2877

LTOS

3900839

15603353

205555492556292306847

606AC3C4D21D0B59

2021-09-02T00:18:52

Team_Inspector

Purple

3900839

15603353

205555492556292306847

2200093016775877920311

606AC3C4D21D0B59

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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