M4 740 419 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	12.5738	66.1765%	1000000000	2510175445470	26,290.5233	27.5130%	26,303.0970	75.4823%
Target	2⁶⁵	1.5390	64.6154%	30000	650000	0.0122	2.2818%	1.5512	65.4228%
Difference	+3	+11.0347	+1.5611%	+999970000	+2510174795470	+26,290.5111	+25.2312%	+26,301.5458	+10.0595%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4740419	9480839	7	23.177	1 1	-	1	1	2.358e-13	1.909e-7	3.885e-7
4740419	237020951	9	27.820	25 5²	2008-09-08	25	25	3.792e-12	4.773e-6	9.714e-6
4740419	426637711	9	28.668	45 3² × 5	2008-09-08	9	9	7.617e-12	1.718e-6	3.497e-6
4740419	578331119	9	29.107	61 61	2008-09-08	1	61	1.529e-11	8.150e-7	1.176e-6
4740419	995487991	9	29.891	105 3 × 5 × 7	2008-09-08	5	7	1.543e-11	9.754e-7	1.943e-6
4740419	2994096044591	13	41.445	315805 5 × 7² × 1289	2008-09-30	49	1289	8.380e-8	2.225e-5	2.496e-5
4740419	67740844907735879881	20	65.877	7145027149260 2² × 3 × 5 × 7 × 11 × 13 × 41 × 757 × 3833	2015-02-20	757	3833	1.5390	0.0002	0.0003

exponent	prime factors	composite factor	digits	bits*
4740419	9480839 237020951	2247157476057889	16	50.997
4740419	9480839 426637711	4044883449319529	16	51.845
4740419	9480839 578331119	5483064227928841	16	52.284
4740419	9480839 995487991	9438061369104449	16	53.067
4740419	237020951 426637711	101122075993683161	18	56.489
4740419	237020951 578331119	137076591818274169	18	56.928
4740419	237020951 995487991	235951510335899441	18	57.711
4740419	426637711 578331119	246737864810228609	18	57.776
4740419	426637711 995487991	424712717808228601	18	58.559
4740419	578331119 995487991	575721683786091929	18	58.998
4740419	9480839 2994096044591	28386542549304091849	20	64.622
4740419	237020951 2994096044591	709663491874297226041	21	69.266
4740419	426637711 2994096044591	1277394282978458171201	22	70.114
4740419	578331119 2994096044591	1731578915861786927329	22	70.553
4740419	995487991 2994096044591	2980586656290941006681	22	71.336
4740419	9480839 237020951 426637711	958722121841875066452079	24	79.665
4740419	9480839 237020951 578331119	1299601097697774654147791	25	80.104
4740419	9480839 237020951 995487991	2237018281301498520310999	25	80.888
4740419	9480839 426637711 578331119	2339281971469542995122951	25	80.952
4740419	9480839 426637711 995487991	4026632898792248241276239	25	81.736
4740419	9480839 578331119 995487991	5458324592784848018048431	25	82.175
4740419	237020951 426637711 578331119	58482043365029819432587159	26	85.596
4740419	237020951 426637711 995487991	100665812276700978634419551	27	86.380
4740419	237020951 578331119 995487991	136458101002300789585004479	27	86.819
4740419	426637711 578331119 995487991	245624581343564074224134519	27	87.667
4740419	9480839 67740844907735879881	642240044294213731675100159	27	89.053
4740419	9480839 237020951 2994096044591	6728205310638020238241328399	28	92.442
4740419	9480839 426637711 2994096044591	12110769536439202389391117639	29	93.290
4740419	237020951 67740844907735879881	16055999481575065506216386831	29	93.697
4740419	9480839 578331119 2994096044591	16416820917080148110310949031	29	93.729
4740419	9480839 995487991 2994096044591	28258462213842748842840485359	29	94.513
4740419	426637711 67740844907735879881	28900799012642441985000792391	29	94.545
4740419	578331119 67740844907735879881	39176638637496343168028316839	29	94.984
4740419	995487991 67740844907735879881	67435197605844571421354009071	29	95.767
4740419	237020951 426637711 2994096044591	302769207753517268251781832151	30	97.934
4740419	237020951 578331119 2994096044591	410420481369109722074887469879	30	98.373
4740419	237020951 995487991 2994096044591	706461483811988970088427973631	30	99.157
4740419	426637711 578331119 2994096044591	738756865079134367045367903919	30	99.221
4740419	426637711 995487991 2994096044591	1271630668477110821126417547191	31	100.005
4740419	578331119 995487991 2994096044591	1723766016209208301956809206039	31	100.443
4740419	2994096044591 67740844907735879881	202822595795504382289033195773671	33	107.322
4740419	9480839 237020951 426637711 578331119	554458837534865948239430207946401	33	108.773
4740419	9480839 237020951 426637711 995487991	954396358999625429575371621483289	33	109.556
4740419	9480839 237020951 578331119 995487991	1293737285848552415628304279677881	34	109.995
4740419	9480839 426637711 578331119 995487991	2328727110160734673903069288981441	34	110.843
4740419	237020951 426637711 578331119 995487991	58218171859028414602038950845307569	35	115.487
4740419	9480839 237020951 67740844907735879881	152224346068896662478891062706431209	36	116.874
4740419	9480839 426637711 67740844907735879881	274003822410221957026632927531496049	36	117.722
4740419	9480839 578331119 67740844907735879881	371427403483282192664826419391547921	36	118.161
4740419	9480839 995487991 67740844907735879881	639342251434197840669858522006690569	36	118.944
4740419	9480839 237020951 426637711 2994096044591	2870506112868648904014955013748654689	37	121.111
4740419	9480839 237020951 578331119 2994096044591	3891130506163028848326754045040148481	37	121.550
4740419	9480839 237020951 995487991 2994096044591	6697847587722573695184201381091756409	37	122.333
4740419	237020951 426637711 67740844907735879881	6850094866636372622247215548268383841	37	122.366
4740419	9480839 426637711 578331119 2994096044591	7004034897959995193324038792823508041	37	122.398
4740419	237020951 578331119 67740844907735879881	9285684146842727516708424452109093889	37	122.804
4740419	9480839 426637711 995487991 2994096044591	12056125635293862880257363411692773249	38	123.181
4740419	237020951 995487991 67740844907735879881	15983554667410203476476748937671046521	38	123.588
4740419	9480839 578331119 995487991 2994096044591	16342748073350894228315893036173586721	38	123.620
4740419	426637711 578331119 67740844907735879881	16714231432975598620078089479373715529	38	123.652
4740419	426637711 995487991 67740844907735879881	28770398347390208172982490950724676481	38	124.436
4740419	578331119 995487991 67740844907735879881	38999873291374211930187084561167580449	38	124.875
4740419	237020951 426637711 578331119 2994096044591	175100854718835117933876160731758006969	39	127.041
4740419	237020951 426637711 995487991 2994096044591	301403110363210528555774378258298198641	39	127.825
4740419	237020951 578331119 995487991 2994096044591	408568660463387966686898078940918723089	39	128.264
4740419	426637711 578331119 995487991 2994096044591	735423587455085527069049900528206336729	39	129.112
4740419	9480839 2994096044591 67740844907735879881	1922928376299253972276775194785655189969	40	130.499
4740419	237020951 2994096044591 67740844907735879881	48073204539739050214814204932844681181121	41	135.142
4740419	426637711 2994096044591 67740844907735879881	86531768009272213750262063047893869507081	41	135.990
4740419	578331119 2994096044591 67740844907735879881	117298618784898744578620349539933220167849	42	136.429
4740419	995487991 2994096044591 67740844907735879881	201907458417871704356605637393041434484961	42	137.213
4740419	9480839 237020951 426637711 578331119 995487991	551957114269779095267180364693274967170391	42	138.664
4740419	9480839 237020951 426637711 67740844907735879881	64944646565305920375533668811429275986722599	44	145.542
4740419	9480839 237020951 578331119 67740844907735879881	88036076401068257906782382174109529597492871	44	145.981
4740419	9480839 237020951 995487991 67740844907735879881	151537508449414686117716343921480227027111119	45	146.765
4740419	9480839 426637711 578331119 67740844907735879881	158464937224780941445582533781536017762248831	45	146.829
4740419	9480839 426637711 995487991 67740844907735879881	272767514697472633864531146522777591043447559	45	147.613
4740419	9480839 578331119 995487991 67740844907735879881	369751519695918992061982988603815482256516711	45	148.051
4740419	9480839 237020951 426637711 578331119 2994096044591	1660103012351666020677092525835919851033966991	46	150.218
4740419	9480839 237020951 426637711 995487991 2994096044591	2857554363452830544342199400592025635305339799	46	151.002
4740419	9480839 237020951 578331119 995487991 2994096044591	3873573690299046706695844095848140925692391671	46	151.440
4740419	237020951 426637711 578331119 67740844907735879881	3961623029477969144725196462664252939087048079	46	151.473
4740419	237020951 426637711 995487991 67740844907735879881	6819187176947255509248282511489656958693953431	46	152.256
4740419	9480839 426637711 578331119 995487991 2994096044591	6972432629464085613371803989873939237307435631	46	152.288
4740419	237020951 578331119 995487991 67740844907735879881	9243787056401015808568488390605357588390986999	46	152.695
4740419	426637711 578331119 995487991 67740844907735879881	16638816670321929822323909558939976010169712239	47	153.543
4740419	237020951 426637711 578331119 995487991 2994096044591	174310798086436041412242450089650868255733809279	48	156.932
4740419	9480839 237020951 2994096044591 67740844907735879881	455774312455335037099568891881306234284538040519	48	158.319
4740419	9480839 426637711 2994096044591 67740844907735879881	820393760881260365739820827564931065883644320959	48	159.167
4740419	9480839 578331119 2994096044591 67740844907735879881	1112089319622000628652022376111830931162929345311	49	159.606
4740419	9480839 995487991 2994096044591 67740844907735879881	1914252106159036351660576634615805560680963162279	49	160.389
4740419	237020951 426637711 2994096044591 67740844907735879881	20509841945269076920962390682833763497638239854031	50	163.811
4740419	237020951 578331119 2994096044591 67740844907735879881	27802230175383164878730689515907384320675949604399	50	164.250
4740419	237020951 995487991 2994096044591 67740844907735879881	47856297808196906762593511306859841584029651417911	50	165.033
4740419	426637711 578331119 2994096044591 67740844907735879881	50044014221850801753796245465737012145270133153639	50	165.098
4740419	426637711 995487991 2994096044591 67740844907735879881	86141335893228465438370956867063204936820224964271	50	165.881
4740419	578331119 995487991 2994096044591 67740844907735879881	11676936636125371237899291331522589561905268380135 9	51	166.320
4740419	9480839 237020951 426637711 578331119 67740844907735879881	37559510121172879508107286905889293170761109822258 281	53	174.649
4740419	9480839 237020951 426637711 995487991 67740844907735879881	64651615735501440975045977517949087790607022752808 609	53	175.433
4740419	9480839 237020951 578331119 995487991 67740844907735879881	87638856832021950317492658904698507832963216788612 161	53	175.872
4740419	9480839 426637711 578331119 995487991 67740844907735879881	15774994200183829481475159237887092321628140441428 8521	54	176.720
4740419	9480839 237020951 426637711 578331119 995487991 2994096044591	16526126126190081924268032982655154481428230726309 05081	55	180.109
4740419	237020951 426637711 578331119 995487991 67740844907735879881	39437481507143572826424740736979436658476108662841 19289	55	181.364
4740419	9480839 237020951 426637711 2994096044591 67740844907735879881	19445050939854292996626015111904697548518503229945 1412009	57	186.987
4740419	9480839 237020951 578331119 2994096044591 67740844907735879881	26358846813374954952570019165930584965545304937142 0610761	57	187.426
4740419	9480839 237020951 995487991 2994096044591 67740844907735879881	45371785465556775331416030314501775362369009631933 5907329	57	188.210
4740419	9480839 426637711 578331119 2994096044591 67740844907735879881	47445924175107773344865984206513262849035074393821 3623121	57	188.274
4740419	9480839 426637711 995487991 2994096044591 67740844907735879881	81669213684862027103825946433257064882999772483003 4103369	57	189.058
4740419	9480839 578331119 995487991 2994096044591 67740844907735879881	11070715626030622852175387932826129649950438276385 92660201	58	189.497
4740419	237020951 426637711 578331119 2994096044591 67740844907735879881	11861479842720602011797253960518424534570477111972 144890689	59	192.918
4740419	237020951 426637711 995487991 2994096044591 67740844907735879881	20417301353823445338473316087411301411233024637065 453441721	59	193.702
4740419	237020951 578331119 995487991 2994096044591 67740844907735879881	27676786262611764460349372736235404559454600833700 405272409	59	194.141
4740419	426637711 578331119 995487991 2994096044591 67740844907735879881	49818215179285682939625901022029397554837565005418 582449249	59	194.989
4740419	9480839 237020951 426637711 578331119 995487991 67740844907735879881	37390041273470556385210791254404338526970997157890 263235803471	62	204.540
4740419	9480839 237020951 426637711 578331119 2994096044591 67740844907735879881	11245678069057934965692586544178753954591262765179 2878193295008071	66	216.095
4740419	9480839 237020951 426637711 995487991 2994096044591 67740844907735879881	19357314695008211967936601562085647546037309806705 0996542952683919	66	216.878
4740419	9480839 237020951 578331119 995487991 2994096044591 67740844907735879881	26239915459323385835449428666323733672805499831357 9316622460871151	66	217.317
4740419	9480839 426637711 578331119 995487991 2994096044591 67740844907735879881	47231847738216369495563988781979617148440862496840 7707809555439911	66	218.165
4740419	237020951 426637711 578331119 995487991 2994096044591 67740844907735879881	11807960738916928071034606644473279758404674308108 632565192907215799	68	222.809
4740419	9480839 237020951 426637711 578331119 995487991 2994096044591 67740844907735879881	11194937468399242941605966902458140519139361396261 4339860750957254928575361	75	245.986

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2015-02-20	pdazzl	Manual testing	50000	50000			67740844907735879881	20	65.877	0.010	1.248	0.019	0.602%
2019-08-27	alpertron	Manual testing	30000000	1000000000	12	-	skipped known factor: 9480839 skipped known factor: 237020951 skipped known factor: 426637711 skipped known factor: 578331119 skipped known factor: 995487991 skipped known factor: 2994096044591 skipped known factor: 67740844907735879881	-	-	15.82	-	-	12.896%
2021-09-28	Seth_Tr	Manual testing	1000000000	251000000000		-	skipped known factor: 9480839 skipped known factor: 237020951 skipped known factor: 426637711 skipped known factor: 578331119 skipped known factor: 995487991 skipped known factor: 2994096044591 skipped known factor: 67740844907735879881	-	-	2,791	-	-	23.673%
2021-12-25	Seth_Tr	Manual testing	1000000000	2510175445470		-	skipped known factor: 9480839 skipped known factor: 237020951 skipped known factor: 426637711 skipped known factor: 578331119 skipped known factor: 995487991 skipped known factor: 2994096044591 skipped known factor: 67740844907735879881	-	-	26,291	-	-	27.513%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08	Will Edgington	Manual testing	?	?	237020951	27.820	9	2.04106e-14	2.800	9.15476e-14
2008-09-08	Will Edgington	Manual testing	?	?	426637711	28.668	9	7.34780e-14	2.800	3.29571e-13
2008-09-08	Will Edgington	Manual testing	?	?	578331119	29.107	9	1.99207e-13	2.800	8.93505e-13
2008-09-08	Will Edgington	Manual testing	?	?	995487991	29.891	9	3.42897e-13	2.800	1.53800e-12
2008-09-30	markr	Manual testing	?	?	2994096044591	41.445	13	2.20040e-8	2.800	9.86945e-8
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	9480839 237020951	50.997	16	3.92838e-5	2.799	0.000
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	237020951	27.820	9	3.79228e-12	2.800	1.70095e-11
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	426637711	28.668	9	7.61722e-12	2.800	3.41656e-11
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	578331119 995487991	58.998	18	0.009	2.783	0.039
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	578331119	29.107	9	1.52867e-11	2.800	6.85655e-11
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	9480839	23.177	7	2.35793e-13	2.800	1.05760e-12
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	995487991	29.891	9	1.54304e-11	2.800	6.92100e-11
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	237020951 578331119	56.928	18	0.003	2.795	0.013
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	426637711 578331119	57.776	18	0.005	2.791	0.024
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	2994096044591	41.445	13	8.38023e-8	2.800	3.75879e-7
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	426637711 995487991	58.559	18	0.013	2.783	0.059
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	9480839 995487991	53.067	16	0.000	2.799	0.002
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	237020951 426637711	56.489	18	0.003	2.795	0.015
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	237020951 995487991	57.711	18	0.007	2.791	0.033
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	9480839 426637711	51.845	16	0.000	2.799	0.001
2022-12-20	LordJulius	Manual testing	2¹	2⁶³	9480839 578331119	52.284	16	0.000	2.799	0.001
2022-12-20	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.414	-	-
2022-12-20	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	0.788	-	-
2022-12-20	LordJulius	Manual testing	2⁶⁵	2⁶⁶	67740844907735879881	65.877	20	-	1.260	-
2019-06-18	Seth_Tr	Manual testing	2⁶⁶	2⁶⁷		-	-	3.153	-	-
2019-12-28	Seth_Tr	Manual testing	2⁶⁷	2⁶⁸		-	-	6.306	-	-

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	0.593

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-05-04	ATH	ec2-ECMCF	50000	5000000						3	0.593

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 = 1000000000, B2 = 2510175445470 (P-1 stage 2)

B1 = 1000000000, B2 = 251000000000 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

B1 = 30000000, B2 = 1000000000 (P-1 stage 2)

B1 = 30000000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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

Total ECM effort:	0.593 GHz-days
Estimated T-Level:	0.577