M4 257 666 431 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷⁹	28.7559	59.4937%	-	-	-	-	28.7559	59.4937%
Target	2⁹²	235,568.9839	65.2174%	20000000	9600000000	212,689.8229	4.2615%	448,258.8068	66.6996%
Difference	-13	-235,540.2279	-5.7237%	-20000000	-9600000000	-212,689.8229	-4.2615%	-448,230.0509	-7.2060%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4257666431	8515332863	10	32.987	1 1	2012-08-20	1	1	1.347e-13	0.0004	0.0008
4257666431	178821990103	12	37.380	21 3 × 7	2012-08-20	3	7	4.515e-12	0.0013	0.0024
4257666431	8591970857759	13	42.966	1009 1009	2019-07-13	1	1009	1.930e-10	0.0219	0.0401
4257666431	194898938545457	15	47.470	22888 2³ × 2861	2019-07-13	8	2861	6.584e-9	0.0641	0.1142
4257666431	363885719191847	15	48.370	42733 151 × 283	2019-07-13	151	283	1.537e-8	0.0621	0.1206
4257666431	8663950966440487	16	52.944	1017453 3 × 339151	2019-07-13	3	339151	2.124e-7	7.2529	13.544

exponent	prime factors	composite factor	digits	bits*
4257666431	8515332863 178821990103	1522728768951136654889	22	70.367
4257666431	8515332863 8591970857759	73163491803013511234017	23	75.954
4257666431	178821990103 8591970857759	1536433327691444318759177	25	80.346
4257666431	8515332863 194898938545457	1659629336359947411453391	25	80.457
4257666431	8515332863 363885719191847	3098608023010724560767961	25	81.358
4257666431	178821990103 194898938545457	34852216059660916869612071	26	84.849
4257666431	178821990103 363885719191847	65070768475947501392290241	26	85.750
4257666431	8515332863 8663950966440487	73776426387951289084824281	26	85.931
4257666431	178821990103 8663950966440487	1549304953973698051452500161	28	90.324
4257666431	8591970857759 194898938545457	1674566000190728808102650863	28	90.436
4257666431	8591970857759 363885719191847	3126495494851024276869490873	28	91.337
4257666431	194898938545457 363885719191847	70920940422341211291713289079	29	95.840
4257666431	8591970857759 8663950966440487	74440414216709588112415688633	29	95.910
4257666431	194898938545457 8663950966440487	1688594846969137258804534717559	31	100.414
4257666431	363885719191847 8663950966440487	3152688028466094483763861109489	31	101.314
4257666431	8515332863 178821990103 8591970857759	13083241207099403731464667290933751	35	113.333
4257666431	8515332863 178821990103 194898938545457	296778220761206974056518754247789273	36	117.837
4257666431	8515332863 178821990103 363885719191847	554099253223900183668507344021489983	36	118.738
4257666431	8515332863 178821990103 8663950966440487	13192847389380933455172539504476090943	38	123.311
4257666431	8515332863 8591970857759 194898938545457	14259486892686577287557323571119210769	38	123.423
4257666431	8515332863 8591970857759 363885719191847	26623149833326374314037586392935459399	38	124.324
4257666431	178821990103 8591970857759 194898938545457	299449224712926803034889218831450408889	39	127.816
4257666431	178821990103 8591970857759 363885719191847	559086146437323950697768828714254829919	39	128.716
4257666431	8515332863 194898938545457 363885719191847	603915414653227215911552850068227703177	39	128.828
4257666431	8515332863 8591970857759 8663950966440487	633884905514879559380847451733360446279	39	128.897
4257666431	178821990103 194898938545457 363885719191847	12682223706299352725695785625598515985137	41	133.220
4257666431	178821990103 8591970857759 8663950966440487	13311583014323662462663604724152255599199	41	133.290
4257666431	8515332863 194898938545457 8663950966440487	14378947192688750446655990573854575841417	41	133.401
4257666431	8515332863 363885719191847 8663950966440487	26846187975584013838857426437399322837007	41	134.302
4257666431	178821990103 194898938545457 8663950966440487	301957891012691862440393056874855398318577	42	137.793
4257666431	178821990103 363885719191847 8663950966440487	563769947424210530046684065510108557387367	42	138.694
4257666431	8591970857759 194898938545457 363885719191847	609350653313617952909036884736794757113961	42	138.806
4257666431	8591970857759 194898938545457 8663950966440487	14508357715720845594931004132144296028690281	44	143.380
4257666431	8591970857759 363885719191847 8663950966440487	27087803664186360430713320035701944744175151	44	144.281
4257666431	194898938545457 363885719191847 8663950966440487	614455550313011337836265271849292211880541473	45	148.784
4257666431	8515332863 178821990103 8591970857759 194898938545457	2549909823997857346796520300679848124767289019207	49	160.803
4257666431	8515332863 178821990103 8591970857759 363885719191847	4760804636005775007153702687927512189765736328097	49	161.704
4257666431	8515332863 178821990103 194898938545457 363885719191847	10799335630216853838074594787826205721226791565723 1	51	166.207
4257666431	8515332863 178821990103 8591970857759 8663950966440487	11335256030042288268683890382161575191943500117673 7	51	166.277
4257666431	8515332863 178821990103 194898938545457 8663950966440487	25712719525825473663313543758434842516751336714959 51	52	170.781
4257666431	8515332863 178821990103 363885719191847 8663950966440487	48006887604731621283371777472166722574181676361417 21	52	171.682
4257666431	8515332863 8591970857759 194898938545457 363885719191847	51888236432519707998331082342783715005386151394003 43	52	171.794
4257666431	178821990103 8591970857759 194898938545457 363885719191847	10896529649610437373022291386166506381657502278512 7983	54	176.186
4257666431	8515332863 8591970857759 194898938545457 8663950966440487	12354349524483732822866476570403711863110674064800 4503	54	176.367
4257666431	8515332863 8591970857759 363885719191847 8663950966440487	23066166472813793113201596863184910335308479113828 7313	54	177.268
4257666431	178821990103 8591970857759 194898938545457 8663950966440487	25944133998514167384875431678861594086103556330342 88943	55	180.760
4257666431	178821990103 8591970857759 363885719191847 8663950966440487	48438949587491404804886081326545647697007417190205 30553	55	181.660
4257666431	8515332863 194898938545457 363885719191847 8663950966440487	52322935404331353815687449825639067551163338352713 27199	55	181.772
4257666431	178821990103 194898938545457 363885719191847 8663950966440487	10987816433680673200668341787711673642045716630308 7041719	57	186.164
4257666431	8591970857759 194898938545457 363885719191847 8663950966440487	52793841816776624052873482588680265218882942902131 83339007	58	191.750
4257666431	8515332863 178821990103 8591970857759 194898938545457 363885719191847	92787577017981632510300107472185475381627349562717 4101300805329	63	209.173
4257666431	8515332863 178821990103 8591970857759 194898938545457 8663950966440487	22092293683962328270351253253632139454996406484094 049042165433809	65	213.747
4257666431	8515332863 178821990103 8591970857759 363885719191847 8663950966440487	41247377927156585306508255129122478810394752635450 635989656463239	65	214.648
4257666431	8515332863 178821990103 194898938545457 363885719191847 8663950966440487	93564914370332496553614524388617384132842789370453 3304699252711497	66	219.151
4257666431	8515332863 8591970857759 194898938545457 363885719191847 8663950966440487	44955713618642161152762981586864737421790981184467 579362490376887041	68	224.738
4257666431	178821990103 8591970857759 194898938545457 363885719191847 8663950966440487	94406998588589770057446936521841252068025007443605 3280808034247847721	69	229.130
4257666431	8515332863 178821990103 8591970857759 194898938545457 363885719191847 8663950966440487	80390701757861308579579129644310973100392005739035 20694083621225127185650955223	79	262.117

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-07-14			2⁴²	2⁴³	8591970857759	42.966	13	5.53719e-11	2,343,600	3.678
2019-07-14			2⁴⁷	2⁴⁸	194898938545457	47.470	15	2.18080e-9	249,604	4.63500e-9
2019-07-14			2⁴⁸	2⁴⁹	363885719191847	48.370	15	6.56337e-9	249,604	1.39496e-8
2019-07-14			2⁵²	2⁵³	8663950966440487	52.944	16	7.14631e-8	249,604	1.51885e-7
TF systematically completed to 64 but no per-exponent detailed record exists
2022-01-27	ramgeis	r4mg31s	2⁷⁰	2⁷¹	178821990103	37.380	12	0.056	2,343,600	0.115
2022-01-27	ramgeis	r4mg31s	2⁷⁰	2⁷¹	8515332863	32.987	10	0.056	2,343,600	3.678
2022-02-03	ramgeis	r4mg31s	2⁷⁵	2⁷⁶	8515332863	32.987	10	1.797	2,343,600	3.678
2022-02-03	ramgeis	r4mg31s	2⁷⁵	2⁷⁶	8591970857759	42.966	13	1.797	2,343,600	3.678
2022-02-06	ramgeis	r4mg31s	2⁷⁶	2⁷⁷		-	-	3.595	-	-
2022-04-07	ramgeis	r4mg31s	2⁷⁷	2⁷⁸		-	-	7.189	-	-
2022-04-27	ramgeis	r4mg31s	2⁷⁸	2⁷⁹		-	-	14.38	-	-

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

10⁰

10¹

10²

10³

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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