M4842923 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	6.1355	65.6716%	-	-	-	-	6.1355	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0634	62.2951%	20000	450000	0.0087	3.2295%	0.0722	63.5128%	1.2177%
GPU72	2⁶⁵	1.5065	64.6154%	32000	650000	0.0132	2.3257%	1.5197	65.4383%	0.8229%
Difference	+2	+4.6291	+1.0563%	-32000	-650000	-0.0132	-2.3257%	+4.6159	+0.2333%	+0.2333%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.1355

65.6716%

6.1355

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0634

62.2951%

20000

450000

0.0087

3.2295%

0.0722

63.5128%

1.2177%

GPU72

2⁶⁵

1.5065

64.6154%

32000

650000

0.0132

2.3257%

1.5197

65.4383%

0.8229%

Difference

+4.6291

+1.0563%

-32000

-650000

-0.0132

-2.3257%

+4.6159

+0.2333%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4842923	9685847	7	23.207	1 1	-	1	1	2.308e-13	2.010e-7	4.090e-7
4842923	15933216671	11	33.891	1645 5 × 7 × 47	2008-09-08	7	47	3.204e-10	1.845e-6	2.863e-6
4842923	7385451259828409	16	52.714	762499348 2² × 13 × 14663449	2014-08-21	13	14663449	0.0001	0.1606	0.2999
4842923	154509699534599694846049	24	77.032	15952111930604688 2⁴ × 3 × 3137 × 47431 × 2233573	2021-07-20	47431	2233573	9,258.7	0.0335	0.0457
4842923	15371117823267478820386441	26	83.668	1586966984945608140 2² × 3² × 5 × 7 × 2069 × 17939 × 33934279	2021-07-20	17939	33934279	514,811	0.3750	0.6940

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4842923

9685847

23.207

1
1

2.308e-13

2.010e-7

4.090e-7

4842923

15933216671

33.891

1645
5 × 7 × 47

2008-09-08

3.204e-10

1.845e-6

2.863e-6

4842923

7385451259828409

52.714

762499348
2² × 13 × 14663449

2014-08-21

14663449

0.0001

0.1606

0.2999

4842923

154509699534599694846049

77.032

15952111930604688
2⁴ × 3 × 3137 × 47431 × 2233573

2021-07-20

47431

2233573

9,258.7

0.0335

0.0457

4842923

15371117823267478820386441

83.668

1586966984945608140
2² × 3² × 5 × 7 × 2069 × 17939 × 33934279

2021-07-20

17939

33934279

514,811

0.3750

0.6940

exponent	prime factors	composite factor	digits	bits*
4842923	9685847 15933216671	154326698893155337	18	57.099
4842923	9685847 7385451259828409	71534350928655215827423	23	75.921
4842923	15933216671 7385451259828409	117673995135955958878206439	27	86.605
4842923	9685847 154509699534599694846049	1496557309708103850525519168503	31	100.239
4842923	9685847 15371117823267478820386441	148882295455141839930003548400527	33	106.876
4842923	9685847 15933216671 7385451259828409	1139772312765613616432599202568833	34	109.812
4842923	15933216671 154509699534599694846049	2461836520455884799232580705282879	34	110.923
4842923	15933216671 15371117823267478820386441	244911350753590625233120656403557911	36	117.560
4842923	7385451259828409 154509699534599694846049	1141123855083518256043526596833411606041	40	129.746
4842923	9685847 15933216671 154509699534599694846049	23844971876148070414992494126522057713513	41	134.131
4842923	7385451259828409 15371117823267478820386441	113522641492821713292634064412096730202369	42	136.382
4842923	9685847 15933216671 15371117823267478820386441	2372173871962613496642346010464432181585617	43	140.767
4842923	9685847 7385451259828409 154509699534599694846049	11052751068389130049744423957359109304137401727	47	152.953
4842923	9685847 7385451259828409 15371117823267478820386441	1099562936535322713230319774883713877940425171543	49	159.589
4842923	154509699534599694846049 15371117823267478820386441	2374986796383988246788243183378958508858182021609	49	160.700
4842923	15933216671 7385451259828409 154509699534599694846049	18181773631492501174525564474298009611177345509511	50	163.637
4842923	15933216671 7385451259828409 15371117823267478820386441	18087808439693832490649793765933074357249749544935 99	52	170.273
4842923	9685847 154509699534599694846049 15371117823267478820386441	23003758736795463408189164873001535136148495759455 467823	56	183.908
4842923	9685847 15933216671 7385451259828409 154509699534599694846049	17610587758327074802377491508668595349839325847126 0590817	57	186.844
4842923	9685847 15933216671 7385451259828409 15371117823267478820386441	17519574511218318834806283299838157046394441488056 962393353	59	193.481
4842923	15933216671 154509699534599694846049 15371117823267478820386441	37841179217550244051194498496215731823956486961453 001043639	59	194.592
4842923	7385451259828409 154509699534599694846049 15371117823267478820386441	17540349227429963081689096644617898740655202703308 051966070090081	65	213.414
4842923	9685847 15933216671 154509699534599694846049 15371117823267478820386441	36652387220077137869253007967607565743987346736612 8665799527677233	66	217.799
4842923	9685847 7385451259828409 154509699534599694846049 15371117823267478820386441	16989313894345482562488909166798234066347897313822 8185211404083800783607	72	236.622
4842923	15933216671 7385451259828409 154509699534599694846049 15371117823267478820386441	27947418472564905825808324949695606663959738117523 2120434322285633060940351	75	247.305
4842923	9685847 15933216671 7385451259828409 154509699534599694846049 15371117823267478820386441	27069441937023737539818808678903434271929443756639 78508012419207332126409915912297	82	270.513

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-07-20T08:42:19	ATH	ec2-P_1	500000	50000000	2	7	154509699534599694846049	P+1P-1	24	77.032	0.650
2021-07-20T08:42:19	ATH	ec2-P_1	500000	50000000	2	7	15371117823267478820386441	P-1	26	83.668	0.650

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-07-20T08:42:19

ATH

ec2-P_1

500000

50000000

154509699534599694846049

P+1P-1

77.032

0.650

2021-07-20T08:42:19

ATH

ec2-P_1

500000

50000000

15371117823267478820386441

P-1

83.668

0.650

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-09-08T00:15:00	Will Edgington	Manual testing	?	?	15933216671	33.891	11	8.41337e-11	1.428	1.78936e-10
2014-08-21T11:33:00	TJAOI	Manual testing	?	?	7385451259828409	52.714	16	1.84486e-5	1.427	3.92296e-5

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-09-08T00:15:00

Will Edgington

Manual testing

15933216671

33.891

8.41337e-11

1.428

1.78936e-10

2014-08-21T11:33:00

TJAOI

Manual testing

7385451259828409

52.714

1.84486e-5

1.427

3.92296e-5

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

Digits

Curves

Complete

FacMiss

11000

3 / 100

0.030

97.030%

50000

3 / 280

0.011

98.932%

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

Digits

Complete

FacMiss

11000

0.097

90.776%

50000

0.009

99.129%

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.627

factor

curves

GHz-days

50000

5000000

0.627

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

Total ECM effort:	0.627 GHz-days
Estimated T-Level:	0.150

Total ECM effort:	0.627 GHz-days
Estimated T-Level:	0.150

Old Calculation Method

New Calculation Method