M1333691 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	22.2795	68.6567%	500000	15000000	0.0714	4.8785%	22.3509	70.1858%	1.5291%
PrimeNet	2⁵⁶	0.0072	62.5000%	6000	100000	0.0006	2.6067%	0.0078	63.4775%	0.9775%
GPU72	2⁶⁰	0.1152	65.0000%	5500	40000	0.0004	0.9789%	0.1156	65.3426%	0.3426%
Difference	+7	+22.1643	+3.6567%	+494500	+14960000	+0.0710	+3.8996%	+22.2353	+4.8432%	+4.8432%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

22.2795

68.6567%

500000

15000000

0.0714

4.8785%

22.3509

70.1858%

1.5291%

PrimeNet

2⁵⁶

0.0072

62.5000%

6000

100000

0.0006

2.6067%

0.0078

63.4775%

0.9775%

GPU72

2⁶⁰

0.1152

65.0000%

5500

40000

0.0004

0.9789%

0.1156

65.3426%

0.3426%

Difference

+22.1643

+3.6567%

+494500

+14960000

+0.0710

+3.8996%

+22.2353

+4.8432%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1333691	2667383	7	21.347	1 1	-	1	1	2.095e-13	5.536e-8	1.127e-7
1333691	44739998287	11	35.381	16773 3 × 5591	2008-07-15	3	5591	5.596e-9	1.702e-5	3.152e-5
1333691	2703188935969	13	41.298	1013424 2⁴ × 3 × 43 × 491	2008-07-15	43	491	2.978e-7	3.732e-6	4.845e-6
1333691	19178607476436887	17	54.090	7190049073 34429 × 208837	2014-10-31	34429	208837	0.0030	0.0024	0.0039
1333691	36379528116926460189343	23	74.946	13638664472102781 3 × 271 × 630467 × 26608411	2018-05-30	630467	26608411	4,371.9	0.1133	0.1499

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1333691

2667383

21.347

1
1

2.095e-13

5.536e-8

1.127e-7

1333691

44739998287

35.381

16773
3 × 5591

2008-07-15

5591

5.596e-9

1.702e-5

3.152e-5

1333691

2703188935969

41.298

1013424
2⁴ × 3 × 43 × 491

2008-07-15

491

2.978e-7

3.732e-6

4.845e-6

1333691

19178607476436887

54.090

7190049073
34429 × 208837

2014-10-31

34429

208837

0.0030

0.0024

0.0039

1333691

36379528116926460189343

74.946

13638664472102781
3 × 271 × 630467 × 26608411

2018-05-30

630467

26608411

4,371.9

0.1133

0.1499

exponent	prime factors	composite factor	digits	bits*
1333691	2667383 44739998287	119338710850772921	18	56.728
1333691	2667383 2703188935969	7210440213591799127	19	62.645
1333691	2667383 19178607476436887	51156691546320652956721	23	75.437
1333691	44739998287 2703188935969	120940668364690412685103	24	76.679
1333691	44739998287 19178607476436887	858050865642831717243612569	27	89.471
1333691	2703188935969 19178607476436887	51843399537596536808912688503	29	95.388
1333691	2667383 36379528116926460189343	97038134847111652159230299369	29	96.293
1333691	2667383 44739998287 2703188935969	322595082804613007059228095449	30	98.026
1333691	44739998287 36379528116926460189343	1627620025633158164576179515655441	34	110.326
1333691	2667383 44739998287 19178607476436887	2288750292150973394436419025136927	34	110.818
1333691	2703188935969 36379528116926460189343	98340737901448756137851742443178367	35	116.243
1333691	2667383 2703188935969 19178607476436887	138286202588792863142967953797197649	36	116.735
1333691	19178607476436887 36379528116926460189343	697708689932531754429969685741009495241	39	129.036
1333691	44739998287 2703188935969 19178607476436887	2319473606504325648927886129956784594361	40	130.769
1333691	2667383 44739998287 36379528116926460189343	4341485986833450324501703445007557180903	40	131.673
1333691	2667383 2703188935969 36379528116926460189343	262312412485780087493251394313312442103561	42	137.590
1333691	2667383 19178607476436887 36379528116926460189343	1861056298478306348726675830260911130444424303	46	150.383
1333691	44739998287 2703188935969 36379528116926460189343	4399764445253133324425767692767765334415457329	46	151.624
1333691	2667383 44739998287 2703188935969 19178607476436887	6186924466938327662414211688982517961660427263	46	152.116
1333691	44739998287 19178607476436887 36379528116926460189343	31215485592406484838769948401514693142733074652167	50	164.417
1333691	2703188935969 19178607476436887 36379528116926460189343	18860384111550454556558545569231647687484445592235 29	52	170.334
1333691	2667383 44739998287 2703188935969 36379528116926460189343	11735856885272638526306777505637960201009105816600 007	53	172.971
1333691	2667383 44739998287 19178607476436887 36379528116926460189343	83263655605929986748692701277077466739142776864921 168961	56	185.764
1333691	2667383 2703188935969 19178607476436887 36379528116926460189343	50307867952619786126436802956093820103585322937153 34454607	58	191.681
1333691	44739998287 2703188935969 19178607476436887 36379528116926460189343	84381355284292935377450067338263535744424160713575 157510094823	62	205.715
1333691	2667383 44739998287 2703188935969 19178607476436887 36379528116926460189343	22507739260228314284590889296693940476456935107665 8244364749259258209	69	227.062

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:05:08	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 2667383 skipped known factor: 44739998287 skipped known factor: 2703188935969 skipped known factor: 19178607476436887	-	-	0.071	-	-	4.878%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:05:08

alpertron

Manual testing

500000

15000000

skipped known factor: 2667383
skipped known factor: 44739998287
skipped known factor: 2703188935969
skipped known factor: 19178607476436887

0.071

-

-

4.878%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T09:58:00	J Feitsma	Manual testing	?	?	2703188935969	41.298	13	7.81624e-8	0.111	1.69886e-7
2008-07-15T09:58:00	J Feitsma	Manual testing	?	?	44739998287	35.381	11	2.16400e-9	0.111	4.70347e-9
2014-10-31T12:49:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	19178607476436887	54.090	17	0.001	0.107	0.003

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T09:58:00

J Feitsma

Manual testing

2703188935969

41.298

7.81624e-8

0.111

1.69886e-7

2008-07-15T09:58:00

J Feitsma

Manual testing

44739998287

35.381

2.16400e-9

0.111

4.70347e-9

2014-10-31T12:49:00

TJAOI

Manual testing

2⁵⁴

2⁵⁵*

19178607476436887

54.090

0.001

0.107

0.003

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.289 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	304 / 100	3.040	4.711%
25	50000	304 / 280	1.086	33.700%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.289 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.360	0.000%
25	50000	1.366	25.525%
30	250000	0.114	89.267%
35	1000000	0.008	99.234%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.71
50000	5000000	36379528116926460189343	3	0.140
250000	35000000		50	13.44

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-09T12:39:14	Chang Chia-Tche	exbpc13	50000	5000000						3	0.140
2018-05-30T06:15:45	Chang Chia-Tche	exbpc13	50000	5000000	36379528116926460189343	74.946	3	2		3	0.140
2018-07-27T12:43:55	TJAOI	Manual testing	50000	5000000						189	8.821
2018-07-27T12:46:49	TJAOI	Manual testing	50000	5000000						59	2.754
2021-07-16T08:44:39	TJAOI	Manual testing	250000	35000000						50	13.44

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T05:04:24

Oliver Kruse

GTX-0

2667383

44739998287

2703188935969

19178607476436887

63B524221FE31C58

2017-09-30T19:23:46

alpertron

Manual testing

2667383

44739998287

2703188935969

19178607476436887

63B524221FE31C__

2017-10-18T05:45:22

Oliver Kruse

Threadripper

2667383

44739998287

2703188935969

19178607476436887

63B524221FE31C__

2018-06-01T19:28:46

M Graber

4fbe3b4e25

2667383

44739998287

2703188935969

19178607476436887

36379528116926460189343

4A89AF6B06515F__

2018-06-05T02:51:03

-Anonymous-

2667383

44739998287

2703188935969

19178607476436887

36379528116926460189343

4A89AF6B06515F__

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