Gaps between Prime Septuplets

← Record Gaps Between Prime Septuplets

References: OEIS A201051 & OEIS A201251

Pattern d: d = 0, 2, 6, 8, 12, 18, 20
_{Gap end} merit = 53.9719483 ·_∫dt / log⁷ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime Septuplet	Merit	Who	When
1	165690	11	165701	1.688141	Alexei Kourbatov	2013
2	903000	165701	1068701	0.718936	Alexei Kourbatov	2013
3	10831800	1068701	11900501	2.814128	Alexei Kourbatov	2013
4	13773480	25658441	39431921	1.611268	Alexei Kourbatov	2013
5	22813770	45002591	67816361	2.142501	Alexei Kourbatov	2013
6	31090080	93625991	124716071	2.259459	Alexei Kourbatov	2013
7	43751820	257016491	300768311	2.246603	Alexei Kourbatov	2013
8	60881310	367438061	428319371	2.753924	Alexei Kourbatov	2013
9	86746170	575226131	661972301	3.362567	Alexei Kourbatov	2013
10	118516860	1228244651	1346761511	3.580671	Alexei Kourbatov	2013
11	239951250	1459270271	1699221521	6.775938	Alexei Kourbatov	2013
12	281573040	2923666841	3205239881	6.406507	Alexei Kourbatov	2013
13	359932650	10180589591	10540522241	5.600354	Alexei Kourbatov	2013
14	384903750	15821203241	16206106991	5.253821	Alexei Kourbatov	2013
15	518385000	23393094071	23911479071	6.305616	Alexei Kourbatov	2013
16	902801550	37846533071	38749334621	9.548660	Alexei Kourbatov	2013
17	1027007520	158303571521	159330579041	7.302347	Alexei Kourbatov	2013
18	1086331680	350060308511	351146640191	6.250454	Alexei Kourbatov	2013
19	1329198570	382631592641	383960791211	7.474687	Alexei Kourbatov	2013
20	2176467090	711854781551	714031248641	10.41354	Alexei Kourbatov	2013
21	2413348560	2879574595811	2881987944371	8.142756	Alexei Kourbatov	2013
22	2724874950	3379186846151	3381911721101	8.842867	Alexei Kourbatov	2013
23	2805731040	5102247756491	5105053487531	8.245032	Alexei Kourbatov	2013
24	3236431380	5987254671311	5990491102691	9.154619	Alexei Kourbatov	2013
25	3558417450	7853481899561	7857040317011	9.439041	Alexei Kourbatov	2013
26	4079266380	11824063534091	11828142800471	9.832192	Alexei Kourbatov	2013
27	5280328410	16348094430581	16353374758991	11.80825	Alexei Kourbatov	2013
28	6089169450	44226969237161	44233058406611	10.87031	Alexei Kourbatov	2013
29	8106605220	54763336591961	54771443197181	13.80121	Alexei Kourbatov	2013
30	8192466870	154325181803321	154333374270191	11.13086	Alexei Kourbatov	2013
31	8398194420	157436722520921	157445120715341	11.36168	Alexei Kourbatov	2013
32	8579120550	281057032201481	281065611322031	10.26309	Alexei Kourbatov	2013
33	9001280190	294887168565161	294896169845351	10.65992	Alexei Kourbatov	2013
34	11138672370	309902902299701	309914040972071	13.05432	Alexei Kourbatov	2013
35	12218589390	419341934631071	419354153220461	13.44350	Alexei Kourbatov	2013
36	13164383820	854077393259801	854090557643621	12.51222	Alexei Kourbatov	2013
37	13412112000	1287032740322501	1287046152434501	11.73238	Norman Luhn	11 Nov 2022
38	14627769870	1287837427840961	1287852055610831	12.79418	Norman Luhn	11 Nov 2022
39	16201309950	1546705949563121	1546722150873071	13.65910	Norman Luhn	11 Nov 2022
40	16834460790	1562479425044381	1562496259505171	14.16411	Norman Luhn	11 Nov 2022
41	17565492840	3584511791361491	3584529356854331	12.54122	Norman Luhn	11 Nov 2022
42	17861894610	4286223364335161	4286241226229771	12.31599	Norman Luhn	11 Nov 2022
43	18296731530	4256202388709261	4256220685440791	12.63307	Norman Luhn	11 Nov 2022
44	19492997160	4574826520578311	4574846013575471	13.27155	Norman Luhn	11 Nov 2022
45	22169881020	5423096204411771	5423118374292791	14.60494	Norman Luhn	11 Nov 2022
46	24332786100	7158931949610431	7158956282396531	15.19551	Norman Luhn	11 Nov 2022
47	24598007070	9528916676356151	9528941274363221	14.54463	Norman Luhn	11 Nov 2022
48	26886742260	13725091836704861	13725118723447121	14.83678	Norman Luhn	24 Nov 2022
49	28638152340	15773525045646281	15773553683798621	15.39525	Norman Luhn	24 Nov 2022
50	38182265940	19076409136724111	19076447318990051	19.80826	Norman Luhn	24 Nov 2022
51	39828828060	38726750725108541	38726790553936601	18.12573	Norman Luhn	24 Nov 2022
52	42100579290	75229732538414801	75229774638994091	16.98203	Norman Luhn	25 Nov 2022
Maximal gaps below 1.00 · 10¹⁷

Pattern d: d = 0, 2, 8, 12, 14, 18, 20
_{Gap end} merit = 53.9719483 ·_∫dt / log⁷ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime Septuplet	Merit	Who	When
1	83160	5639	88799	0.346488	Alexei Kourbatov	2013
2	195930	88799	284729	0.286450	Alexei Kourbatov	2013
3	341880	284729	626609	0.295756	Alexei Kourbatov	2013
4	5414220	1146779	6560999	1.706593	Alexei Kourbatov	2013
5	9270030	8573429	17843459	1.592096	Alexei Kourbatov	2013
6	18980220	24001709	42981929	2.202832	Alexei Kourbatov	2013
7	25622520	43534019	69156539	2.409908	Alexei Kourbatov	2013
8	36077370	87988709	124066079	2.653196	Alexei Kourbatov	2013
9	51597630	157131419	208729049	3.092750	Alexei Kourbatov	2013
10	92184750	522911099	615095849	3.678877	Alexei Kourbatov	2013
11	125523090	706620359	832143449	4.514596	Alexei Kourbatov	2013
12	140407470	1590008669	1730416139	3.898853	Alexei Kourbatov	2013
13	141896370	2346221399	2488117769	3.484702	Alexei Kourbatov	2013
14	336026460	3357195209	3693221669	7.310985	Alexei Kourbatov	2013
15	403369470	11768282159	12171651629	6.007878	Alexei Kourbatov	2013
16	435390270	30717348029	31152738299	4.897555	Alexei Kourbatov	2013
17	442452570	33788417009	34230869579	4.842449	Alexei Kourbatov	2013
18	627852330	62923039169	63550891499	5.758068	Alexei Kourbatov	2013
19	754383210	68673910169	69428293379	6.749610	Alexei Kourbatov	2013
20	1008582120	88850237459	89858819579	8.397723	Alexei Kourbatov	2013
21	1021464990	163288980299	164310445289	7.202334	Alexei Kourbatov	2013
22	1073692620	196782371699	197856064319	7.199282	Alexei Kourbatov	2013
23	1088148810	421204876439	422293025249	5.964605	Alexei Kourbatov	2013
24	1145336850	427478111309	428623448159	6.253781	Alexei Kourbatov	2013
25	1568502810	487635377219	489203880029	8.274770	Alexei Kourbatov	2013
26	1831427220	994838839439	996670266659	8.047248	Alexei Kourbatov	2013
27	1981464870	1554893017199	1556874482069	7.782617	Alexei Kourbatov	2013
28	2112833100	2088869793539	2090982626639	7.712873	Alexei Kourbatov	2013
29	2124912720	2104286376329	2106411289049	7.742911	Alexei Kourbatov	2013
30	2524750410	2704298257469	2706823007879	8.650213	Alexei Kourbatov	2013
31	2563342320	3550904257709	3553467600029	8.219374	Alexei Kourbatov	2013
32	3703761600	4438966968419	4442670730019	11.25323	Alexei Kourbatov	2013
33	4007885700	9996858589169	10000866474869	10.04573	Alexei Kourbatov	2013
34	4510983120	21937527068909	21942038052029	9.431002	Alexei Kourbatov	2013
35	4684341270	29984058230039	29988742571309	9.123705	Alexei Kourbatov	2013
36	5008335150	30136375346249	30141383681399	9.743596	Alexei Kourbatov	2013
37	5458736640	32779504324739	32784963061379	10.42064	Alexei Kourbatov	2013
38	5459261010	40372176609629	40377635870639	9.946125	Alexei Kourbatov	2013
39	5538301020	42762127106969	42767665407989	9.961421	Alexei Kourbatov	2013
40	5853061830	54620176867169	54626029928999	9.970451	Alexei Kourbatov	2013
41	7142583420	63358011407219	63365153990639	11.77491	Alexei Kourbatov	2013
42	7395601290	79763188368959	79770583970249	11.59123	Alexei Kourbatov	2013
43	7524703830	109974651670769	109982176374599	10.99752	Alexei Kourbatov	2013
44	8171975700	145568747217989	145576919193689	11.24297	Alexei Kourbatov	2013
45	8428843500	196317277557209	196325706400709	10.87851	Alexei Kourbatov	2013
46	8567796510	221953318490999	221961886287509	10.77344	Alexei Kourbatov	2013
47	9121701330	249376874266769	249385995968099	11.19074	Alexei Kourbatov	2013
48	9626062320	290608782523049	290618408585369	11.43488	Alexei Kourbatov	2013
49	11248937910	310213774327979	310225023265889	13.18077	Alexei Kourbatov	2013
50	11485174050	471088826892779	471100312066829	12.33503	Alexei Kourbatov	2013
51	12971201880	631565753063879	631578724265759	13.11353	Alexei Kourbatov	2013
52	15375948840	665514714418439	665530090367279	15.37850	Alexei Kourbatov	2013
53	19295924760	2170156154684039	2170175450608799	15.20693	Norman Luhn	11 Nov 2022
54	20356705950	4646664842384429	4646685199090379	13.81775	Norman Luhn	11 Nov 2022
55	21646799790	5069895255182489	5069916901982279	14.44729	Norman Luhn	11 Nov 2022
56	22126391700	5135889251602379	5135911377994079	14.73046	Norman Luhn	11 Nov 2022
57	22930766670	10177783172013629	10177806102780299	13.39008	Norman Luhn	11 Nov 2022
58	23611242480	10884814410333749	10884838021576229	13.61285	Norman Luhn	11 Nov 2022
59	27155401350	11176819587569549	11176846742970899	15.57786	Norman Luhn	11 Nov 2022
60	28161022890	15264678123669419	15264706284692309	15.23226	Norman Luhn	11 Nov 2022
61	28751240700	20981707666266029	20981736417506729	14.65314	Norman Luhn	11 Nov 2022
62	30097138890	21953477741043839	21953507838182729	15.21036	Norman Luhn	11 Nov 2022
63	35278237890	24106457559841829	24106492838079719	17.52152	Norman Luhn	24 Nov 2022
64	36240351840	24417972248919239	24418008489271079	17.95655	Norman Luhn	24 Nov 2022
65	41722072350	39329943754173209	39329985476245559	18.93363	Norman Luhn	24 Nov 2022
Maximal gaps below 1.00 · 10¹⁷

Record Gaps Between Prime Septuplets Over All Pattern

_{Gap end} merit = 107.9438966 ·_∫dt / log⁷ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime Septuplets	Merit	Who	When
1	5628	11	5639	2.411193	Norman Luhn	17 Jan 2023
2	83160	5639	88799	0.692977	Norman Luhn	17 Jan 2023
3	119028	165701	284729	0.300790	Norman Luhn	17 Jan 2023
4	341880	284729	626609	0.591512	Norman Luhn	17 Jan 2023
5	5414220	1146779	6560999	3.413186	Norman Luhn	17 Jan 2023
6	13773480	25658441	39431921	3.222536	Norman Luhn	17 Jan 2023
7	22813770	45002591	67816361	4.285002	Norman Luhn	17 Jan 2023
8	30440088	93625991	124066079	4.429143	Norman Luhn	17 Jan 2023
9	33424818	327864611	361289429	3.181293	Norman Luhn	17 Jan 2023
10	34863108	367438061	402301169	3.190326	Norman Luhn	17 Jan 2023
11	39869718	575226131	615095849	3.131608	Norman Luhn	17 Jan 2023
12	66303048	1228244651	1294547699	4.033393	Norman Luhn	17 Jan 2023
13	70350000	1519658669	1590008669	3.992120	Norman Luhn	17 Jan 2023
14	109212852	1590008669	1699221521	6.083868	Norman Luhn	17 Jan 2023
15	131165160	3008352029	3139517189	5.962059	Norman Luhn	17 Jan 2023
16	161786520	8436205691	8597992211	5.344403	Norman Luhn	17 Jan 2023
17	228283230	13835037311	14063320541	6.494341	Norman Luhn	17 Jan 2023
18	257159490	15863572589	16120732079	7.023074	Norman Luhn	17 Jan 2023
19	289262610	19763247389	20052509999	7.403026	Norman Luhn	17 Jan 2023
20	350304570	47827797749	48178102319	6.946639	Norman Luhn	17 Jan 2023
21	439508622	81720304649	82159813271	7.497362	Norman Luhn	17 Jan 2023
22	561983940	130121377481	130683361421	8.432725	Norman Luhn	17 Jan 2023
23	571529112	338490796739	339062325851	6.636580	Norman Luhn	17 Jan 2023
24	777665070	378184596059	378962261129	8.770142	Norman Luhn	17 Jan 2023
25	815371200	632131550579	632946921779	8.046174	Norman Luhn	17 Jan 2023
26	908352732	811003946099	811912298831	8.409066	Norman Luhn	17 Jan 2023
27	1063368810	819221051261	820284420071	9.818608	Norman Luhn	17 Jan 2023
28	1211707350	1330453426439	1331665133789	9.897261	Norman Luhn	17 Jan 2023
29	1234420782	2219662600019	2220897020801	8.879064	Norman Luhn	17 Jan 2023
30	1261947498	3618415983641	3619677931139	8.056424	Norman Luhn	17 Jan 2023
31	1468079298	4064130673901	4065598753199	9.113016	Norman Luhn	17 Jan 2023
32	1887408222	4683800652899	4685688061121	11.32278	Norman Luhn	17 Jan 2023
33	1947769572	15457675215119	15459622984691	8.824766	Norman Luhn	17 Jan 2023
34	2478988722	17668104903719	17670583892441	10.89154	Norman Luhn	17 Jan 2023
35	3484084380	18865153070831	18868637155211	15.07907	Norman Luhn	17 Jan 2023
36	3523349172	57075938362349	57079461711521	11.88764	Norman Luhn	17 Jan 2023
37	3668832300	66634278495131	66637947327431	11.96310	Norman Luhn	17 Jan 2023
38	3677810220	99373821578399	99377499388619	10.98935	Norman Luhn	17 Jan 2023
39	3704425998	141387806832731	141391511258729	10.25709	Norman Luhn	17 Jan 2023
40	3974542320	147400207111679	147404181653999	10.90705	Norman Luhn	17 Jan 2023
41	4296334602	178458970788809	178463267123411	11.31756	Norman Luhn	17 Jan 2023
42	5343753870	185072465945441	185077809699311	13.96792	Norman Luhn	17 Jan 2023
43	5372585022	393208334708459	393213707293481	11.98176	Norman Luhn	17 Jan 2023
44	5842028388	503820405016541	503826247044929	12.37540	Norman Luhn	17 Jan 2023
45	6549026022	566548557083219	566555106109241	13.54107	Norman Luhn	17 Jan 2023
46	7247706060	1235175843036251	1235183090742311	12.78544	Norman Luhn	18 Jan 2023
47	7268347422	1703169634352099	1703176902699521	12.02191	Norman Luhn	18 Jan 2023
48	8270089212	2017317988864679	2017326258953891	13.22543	Norman Luhn	18 Jan 2023
49	8425586190	2175705123427931	2175713549014121	13.27353	Norman Luhn	18 Jan 2023
50	9564343950	2710640296617551	2710649860961501	14.42702	Norman Luhn	18 Jan 2023
51	9848718180	3417906881673281	3417916730391461	14.19487	Norman Luhn	19 Jan 2023
52	11447130828	3510982467857981	3510993914988809	16.41216	Norman Luhn	19 Jan 2023
53	12557720952	4534734118206359	4534746675927311	17.12876	Norman Luhn	19 Jan 2023
54	16763556012	8025455431960649	8025472195516661	20.48424	Norman Luhn	19 Jan 2023
Maximal gaps below 1.00 · 10¹⁶