M3 418 073 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	279.7874	69.4444%	20508438	12354931050	105.4643	12.6164%	385.2517	73.2995%
Target	2⁶⁴	1.0413	65.6250%	19000	1600000	0.0160	1.8210%	1.0573	66.2510%
Difference	+8	+278.7460	+3.8194%	+20489438	+12353331050	+105.4483	+10.7954%	+384.1944	+7.0485%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3418073	5434736071	10	32.340	795 3 × 5 × 53	-	5	53	1.962e-10	1.160e-6	1.550e-6
3418073	32758811633	11	34.931	4792 2³ × 599	2008-09-07	8	599	6.945e-10	6.122e-6	9.290e-6
3418073	112222172737	12	36.708	16416 2⁵ × 3³ × 19	2008-09-07	32	32	4.160e-9	4.873e-6	9.918e-6
3418073	5633203060673	13	42.357	824032 2⁵ × 11 × 2341	2013-12-17	32	2341	2.334e-7	2.403e-5	3.627e-5
3418073	29739203910049	14	44.757	4350288 2⁴ × 3 × 90631	2008-09-30	16	90631	1.111e-6	0.0008	0.0014
3418073	1045910829158799843713	22	69.825	152997146222272 2⁶ × 11 × 103 × 6569 × 321199	2019-08-12	6569	321199	37.593	0.0036	0.0050

exponent	prime factors	composite factor	digits	bits*
3418073	5434736071 32758811633	178035495224959513943	21	67.271
3418073	5434736071 112222172737	609897890139766696327	21	69.047
3418073	32758811633 112222172737	3676265017737371049521	22	71.639
3418073	5434736071 5633203060673	30614971869107154635783	23	74.697
3418073	5434736071 29739203910049	161624724212767539677479	24	77.097
3418073	32758811633 5633203060673	184537037955025877209009	24	77.288
3418073	112222172737 5633203060673	632170286937442497472001	24	79.065
3418073	32758811633 29739203910049	974220979004672266800017	24	79.689
3418073	112222172737 29739203910049	3337398078254384688134113	25	81.465
3418073	5633203060673 29739203910049	167526974488066475781402977	27	87.115
3418073	5434736071 1045910829158799843713	5684249310278848097696203671623	31	102.165
3418073	5434736071 32758811633 112222172737	19979530098452745247542905971991	32	103.978
3418073	32758811633 1045910829158799843713	34262795837327967924544006313329	32	104.756
3418073	112222172737 1045910829158799843713	117374385737357732464768889452481	33	106.533
3418073	5434736071 32758811633 5633203060673	1002910096609675210606218018463639	34	109.628
3418073	5434736071 112222172737 5633203060673	3435678661433338861499410147248071	34	111.404
3418073	5434736071 32758811633 29739203910049	5294633895721626045911388133313207	34	112.028
3418073	5633203060673 1045910829158799843713	5891828084008386493555465656598849	34	112.182
3418073	5434736071 112222172737 29739203910049	18137877719175185178512549606690023	35	113.805
3418073	32758811633 112222172737 5633203060673	20709147349763239229454359450587633	35	113.996
3418073	29739203910049 1045910829158799843713	31104555420081971953685819710171937	35	114.583
3418073	32758811633 112222172737 29739203910049	109329194989871581454904858008536529	36	116.396
3418073	5434736071 5633203060673 29739203910049	910464891115791634975038670088683367	36	119.454
3418073	32758811633 5633203060673 29739203910049	5487984600700966286505136608008431441	37	122.046
3418073	112222172737 5633203060673 29739203910049	18800241069106788190279431937100038049	38	123.822
3418073	5434736071 32758811633 1045910829158799843713	186209252430434955536650317337900844390359	42	137.096
3418073	5434736071 112222172737 1045910829158799843713	637898807978286000857047220186009931142151	42	138.872
3418073	32758811633 112222172737 1045910829158799843713	3845045392909183768949372858452425583511473	43	141.464
3418073	5434736071 5633203060673 1045910829158799843713	32020530612291196343035098243119463837382279	44	144.522
3418073	5434736071 32758811633 112222172737 5633203060673	112548750101412329550117852954308351211609943	45	146.335
3418073	5434736071 29739203910049 1045910829158799843713	169045049313938050753506665780074191625839527	45	146.922
3418073	32758811633 5633203060673 1045910829158799843713	193009286378050032734644867882122357835610417	45	147.114
3418073	5434736071 32758811633 112222172737 29739203910049	594175319624847563390786091692126700077437559	45	148.736
3418073	112222172737 5633203060673 1045910829158799843713	661193748980296896436439204205307156393379713	45	148.890
3418073	32758811633 29739203910049 1045910829158799843713	1018948271934674504649982767948721138225743121	46	149.514
3418073	112222172737 29739203910049 1045910829158799843713	3490620791260028655286119423342354389983881569	46	151.290
3418073	5434736071 32758811633 5633203060673 29739203910049	29825747866522073361824386450326009824533208311	47	154.385
3418073	5434736071 112222172737 5633203060673 29739203910049	102174348281770265528668440317946979920372765479	48	156.162
3418073	5633203060673 29739203910049 1045910829158799843713	175218276793278715658052304994779425299472933601	48	156.940
3418073	32758811633 112222172737 5633203060673 29739203910049	615873555837859809886992872461704450724323824017	48	158.753
3418073	5434736071 32758811633 112222172737 1045910829158799843713	20896806891475908656276886446659774556153025155442 583	53	173.804
3418073	5434736071 32758811633 5633203060673 1045910829158799843713	10489545307167574555457052348539997541647614215732 51607	55	179.453
3418073	5434736071 112222172737 5633203060673 1045910829158799843713	35934135175029390113524675018931176924855389918407 27623	55	181.229
3418073	5434736071 32758811633 29739203910049 1045910829158799843713	55377149279664924860653185784993374482356230804788 17591	55	181.853
3418073	5434736071 112222172737 29739203910049 1045910829158799843713	18970602724443439273377098055652412785310602271636 375399	56	183.630
3418073	32758811633 112222172737 5633203060673 1045910829158799843713	21659921475762631858775820847818078595197597666410 601329	56	183.821
3418073	32758811633 112222172737 29739203910049 1045910829158799843713	11434858898312069144070027590881477073221259822505 1492177	57	186.221
3418073	5434736071 5633203060673 29739203910049 1045910829158799843713	95226508918689404634336936355982120936369552952954 2621671	57	189.279
3418073	5434736071 32758811633 112222172737 5633203060673 29739203910049	33471102290870493362340425976875277444927247634698 46017207	58	191.093
3418073	32758811633 5633203060673 29739203910049 1045910829158799843713	57399425241298727267103030989854442417694284460170 75380433	58	191.871
3418073	112222172737 5633203060673 29739203910049 1045910829158799843713	19663375724974802469163452396105144549171039509627 553435937	59	193.647
3418073	5434736071 32758811633 112222172737 5633203060673 1045910829158799843713	11771595653935472759678273146427071338723339141018 7120139516838359	66	216.161
3418073	5434736071 32758811633 112222172737 29739203910049 1045910829158799843713	62145440121451923191923474698128794135595088921431 7920366716216567	66	218.561
3418073	5434736071 32758811633 5633203060673 29739203910049 1045910829158799843713	31195072681355407196491609419399277324703557640622 475851965272698743	68	224.211
3418073	5434736071 112222172737 5633203060673 29739203910049 1045910829158799843713	10686525733014633454526247993200400899004888157153 9016433766801583527	69	225.987
3418073	32758811633 112222172737 5633203060673 29739203910049 1045910829158799843713	64414882144335436775870882813197093314853078959468 9712994502115855121	69	228.579
3418073	5434736071 32758811633 112222172737 5633203060673 29739203910049 1045910829158799843713	35007788349903362656936542926349619787058498828643 71653263858073723647108769591	79	260.918

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2019-08-12	Jocelyn Larouche	Manual testing	324710	324710			1045910829158799843713	22	69.825	0.049	0.718	0.099	0.973%
2020-04-21	Jocelyn Larouche	Manual testing	752004	34180730	12	-	skipped known factor: 5434736071 skipped known factor: 32758811633 skipped known factor: 112222172737 skipped known factor: 5633203060673 skipped known factor: 29739203910049 skipped known factor: 1045910829158799843713	-	-	0.392	-	-	4.144%
2021-08-04	Jocelyn Larouche	Manual testing	3418073	3418073		-	skipped known factor: 5434736071 skipped known factor: 32758811633 skipped known factor: 112222172737 skipped known factor: 5633203060673 skipped known factor: 29739203910049 skipped known factor: 1045910829158799843713	-	-	0.521	-	-	2.645%
2021-08-10	Jocelyn Larouche	Manual testing	3418073	34180730	12	-	skipped known factor: 5434736071 skipped known factor: 32758811633 skipped known factor: 112222172737 skipped known factor: 5633203060673 skipped known factor: 29739203910049 skipped known factor: 1045910829158799843713	-	-	0.776	-	-	4.846%
2021-08-14	Jocelyn Larouche	Manual testing	3418073	205084380	12	-	skipped known factor: 5434736071 skipped known factor: 32758811633 skipped known factor: 112222172737 skipped known factor: 5633203060673 skipped known factor: 29739203910049 skipped known factor: 1045910829158799843713	-	-	2.194	-	-	6.621%
2021-12-17	Jocelyn Larouche	Manual testing	4380000	621034050		-	skipped known factor: 5434736071 skipped known factor: 32758811633 skipped known factor: 112222172737 skipped known factor: 5633203060673 skipped known factor: 29739203910049 skipped known factor: 1045910829158799843713	-	-	5.784	-	-	7.936%
2022-01-10	Jocelyn Larouche	Manual testing	4380000	1042764450		-	skipped known factor: 5434736071 skipped known factor: 32758811633 skipped known factor: 112222172737 skipped known factor: 5633203060673 skipped known factor: 29739203910049 skipped known factor: 1045910829158799843713	-	-	9.283	-	-	8.486%
2022-02-12	Jocelyn Larouche	Manual testing	5000000	141372000		-	skipped known factor: 5434736071 skipped known factor: 32758811633 skipped known factor: 112222172737 skipped known factor: 5633203060673 skipped known factor: 29739203910049 skipped known factor: 1045910829158799843713	-	-	1.893	-	-	6.451%
2022-03-19	Jocelyn Larouche	Manual testing	5000000	1002168090		-	skipped known factor: 5434736071 skipped known factor: 32758811633 skipped known factor: 112222172737 skipped known factor: 5633203060673 skipped known factor: 29739203910049 skipped known factor: 1045910829158799843713	-	-	9.035	-	-	8.548%
2022-06-10	Jocelyn Larouche	Manual testing	20508438	12354931050		-	skipped known factor: 5434736071 skipped known factor: 32758811633 skipped known factor: 112222172737 skipped known factor: 5633203060673 skipped known factor: 29739203910049 skipped known factor: 1045910829158799843713	-	-	105.5	-	-	12.616%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-07	Will Edgington	Manual testing	?	?	112222172737	36.708	12	1.48177e-9	1.765	7.28395e-9
2008-09-07	Will Edgington	Manual testing	?	?	32758811633	34.931	11	2.49281e-11	1.765	1.22539e-10
2008-09-30	markr	Manual testing	?	?	29739203910049	44.757	14	4.25637e-7	1.765	2.09230e-6
2013-12-17	TJAOI	Manual testing	?	?	5633203060673	42.357	13	6.20350e-8	1.765	3.04946e-7
2022-12-02	LordJulius	Manual testing	2¹	2⁶²	112222172737	36.708	12	4.16009e-9	1.765	2.04498e-8
2022-12-02	LordJulius	Manual testing	2¹	2⁶²	29739203910049	44.757	14	1.11129e-6	1.765	5.46275e-6
2022-12-02	LordJulius	Manual testing	2¹	2⁶²	32758811633	34.931	11	6.94508e-10	1.765	3.41400e-9
2022-12-02	LordJulius	Manual testing	2¹	2⁶²	5434736071	32.340	10	1.96200e-10	1.765	9.64461e-10
2022-12-02	LordJulius	Manual testing	2¹	2⁶²	5633203060673	42.357	13	2.33447e-7	1.765	1.14756e-6
2022-12-02	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.287	-	-
2022-12-02	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.574	-	-
2022-12-02	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.093	-	-
2021-01-20	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.186	-	-
2021-01-20	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.372	-	-
2021-01-20	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.745	-	-
2021-01-21	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	17.49	-	-
2021-01-23	Jocelyn Larouche	Manual testing	2⁶⁹	2⁷⁰	skipped known factors(?)	-	-	34.98	-	-
2022-12-03	LordJulius	Manual testing	2⁶⁹	2⁷⁰	1045910829158799843713	69.825	22	2.665	0.723	5.370
2021-08-14	Jocelyn Larouche	Manual testing	2⁷⁰	2⁷¹		-	-	69.96	-	-
2021-11-04	Jocelyn Larouche	Manual testing	2⁷¹	2⁷²		-	-	139.9	-	-

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.440

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-30	rucio		50000	5000000						3	0.440

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 = 20508438, B2 = 12354931050 (P-1 stage 2)

B1 = 4380000, B2 = 1042764450 (P-1 stage 2)

B1 = 5000000, B2 = 1002168090 (P-1 stage 2)

B1 = 4380000, B2 = 621034050 (P-1 stage 2)

B1 = 20508438 (P-1 stage 1)

B1 = 3418073, B2 = 205084380 (P-1 stage 2)

B1 = 5000000, B2 = 141372000 (P-1 stage 2)

B1 = 3418073, B2 = 34180730 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 4380000 (P-1 stage 1)

B1 = 3418073 (P-1 stage 1)

B1 = 752004, B2 = 34180730 (P-1 stage 2)

B1 = 752004 (P-1 stage 1)

B1 = 324710 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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:	0.440 GHz-days
Estimated T-Level:	0.577