Thread: Top 50 gaps
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Old 2018-07-10, 08:01   #1
robert44444uk
 
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Jun 2003
Oxford, UK

7BB16 Posts
Default Top 50 gaps

We can extend the list given at http://ntheory.org/gaps/top20.pl, to cover the top 50 gaps at varying levels of prime gap length and merit. To qualify, a gap with a rank of 1 means that every gap found to be larger than the rank 1 gap has a smaller merit. I then rank the gaps larger than the rank 1 gap in order of merit and ignore those that are lower than 50th. I then rank the qualifying gaps according to their highest position. I only list gaps starting from 8350 which is the greatest merit gap. Of course, gaps that are not the top merit for their length are not included as there are no records kept of these gaps. The gap list used for this analysis is 3 July 2018 at http://trnicely.net/index.html#TPG

As expected danaj dominates the Top 50 list but with less of a dominant percentage. Only 11 discoverers are on the list, and their discoveries cover 98% of all listed gaps.



Code:
Gapcoin 	3	0.87%	849	0.92%
Jacobsen	166	48.40%	56773	61.68%
M.Jansen	27	7.87%	2559	2.78%
MJandJKA	2	0.58%	2	0.00%
MJPC&JKA	17	4.96%	2594	2.82%
MrtnRaab	28	8.16%	114	0.12%
PierCami	7	2.04%	789	0.86%
RobSmith	34	9.91%	7573	8.23%
Rosnthal	33	9.62%	10996	11.95%
RosntlJA	1	0.29%	8	0.01%
Toni_Key	25	7.29%	9793	10.64%
				
Total    	343	100.00%	92050	100.00%
Total gaps			93945	
				
    	       	  	       97.98%

Code:
Gap  	Merit  	Finder  	Hi rank	8350	15900	18306	26054	26892	66520	70862	71766	77640	120664	157178	309030	512226	1113106	1286500	2332764	4680156	6582144
8350	41.9388	Gapcoin 	1	1																	
15900	39.6202	Jacobsen	1	2	1																
18306	38.0670	Jacobsen	1	3	2	1															
26054	37.0053	Jacobsen	1	5	3	2	1														
26892	36.4206	Jacobsen	1	8	4	3	2	1													
66520	35.4245	M.Jansen	1	16	9	8	4	2	1												
70862	34.8067	Toni_Key	1	21	12	11	5	3	2	1											
71766	34.4576	Jacobsen	1	34	19	18	8	6	3	2	1										
77640	32.6483	Toni_Key	1				20	16	4	3	2	1									
120664	32.3245	MJPC&JKA	1				27	23	7	5	3	2	1								
157178	31.8285	Jacobsen	1				41	36	9	7	5	4	2	1							
309030	31.7822	Rosnthal	1				44	39	10	8	6	5	3	2	1						
512226	29.7175	RobSmith	1						29	22	20	16	7	5	2	1					
1113106	25.9045	MJPC&JKA	1												4	2	1				
1286500	25.8571	Rosnthal	1												5	3	2	1			
2332764	25.7927	MrtnRaab	1												6	4	3	2	1		
4680156	20.3767	MrtnRaab	1												33	5	4	3	2	1	
6582144	13.1829	MrtnRaab	1														5	4	3	2	1
26730	35.7817	Jacobsen	3	11	6	5	3														
109776	32.2502	Jacobsen	3				30	25	8	6	4	3									
157194	30.3829	RobSmith	3						18	14	12	10	5	3							
379304	26.3114	RobSmith	3											43	3						
5103138	10.2203	RobSmith	3														6	5	4	3	
8382	37.8241	Jacobsen	4	4																	
24416	36.0241	Jacobsen	4	9	5	4															
27340	34.7080	Jacobsen	4	24	14	13	6	4													
71046	32.5590	Jacobsen	4				21	17	5	4											
125078	30.4885	Jacobsen	4						17	13	11	9	4								
286764	29.7946	Rosnthal	4						25	19	17	14	6	4							
3311852	14.6838	MJandJKA	5														7	6	5		
27666	34.6593	Gapcoin 	5	28	16	15	7	5													
2079500	22.9896	MrtnRaab	6												14	6	8	7			
2945060	12.8223	MrtnRaab	6														9	8	6		
10716	36.8583	Jacobsen	6	6																	
24818	35.5799	Jacobsen	6	13	7	6															
68202	32.4219	Toni_Key	6				25	21	6												
101616	30.8124	Jacobsen	6						14	10	8	6									
193396	29.5530	Toni_Key	6						32	24	22	18	8	6							
3870360	12.4164	RobSmith	7														10	9	7		
1260182	25.3279	Rosnthal	7												7	7	11				
13692	36.5902	Jacobsen	7	7																	
23548	35.4249	Jacobsen	7	15	8	7															
42242	34.1987	Jacobsen	7	43	21	20	9	7													
76606	31.4202	Jacobsen	7						12	9	7										
84766	30.7110	Jacobsen	7						15	11	9	7									
280364	29.1570	Toni_Key	7						40	32	29	23	9	7							
2765878	12.0114	MJPC&JKA	8														12	10	8		
1151150	23.1376	Rosnthal	8												13	8	13				
984108	25.2886	M.Jansen	8												8	9					
29620	33.5751	Jacobsen	8		32	31	11	8													
99160	30.5264	Jacobsen	8						16	12	10	8									
179548	28.6615	Jacobsen	8							45	41	32	10	8							
2724214	11.8311	MJandJKA	9														14	11	9		
19474	35.1999	Jacobsen	9	17	10	9															
35004	33.5011	Jacobsen	9		34	33	12	9													
165894	28.6020	Toni_Key	9							49	45	35	11	9							
321562	24.5692	Toni_Key	9												9						
3370374	11.2705	MrtnRaab	10														15	12	10		
566040	23.5278	M.Jansen	10												11	10					
9006	35.8500	Jacobsen	10	10																	
24008	34.9648	Jacobsen	10	18	11	10															
26858	33.6621	Gapcoin 	10		27	26	10														
60310	33.2174	Jacobsen	10		48	44	14	10													
262726	28.5665	Rosnthal	10								47	36	12	10							
418250	23.5527	RobSmith	10												10						
2586246	11.2601	MrtnRaab	11														16	13	11		
1113976	22.3878	Rosnthal	11												16	11	17				
51510	33.0719	Toni_Key	11			49	15	11													
69802	31.4615	Jacobsen	11					50	11												
116676	30.3614	Toni_Key	11						19	15	13	11									
278508	28.4694	Rosnthal	11									41	15	11							
2559528	11.1438	MrtnRaab	12														18	14	12		
973764	22.6787	MJPC&JKA	12												15	12					
13024	35.6819	Jacobsen	12	12																	
18840	34.7563	Jacobsen	12	22	13	12															
55982	33.0628	Jacobsen	12			50	16	12													
85686	30.0930	MJPC&JKA	12						22	17	15	12									
265242	28.1789	Toni_Key	12									49	18	12							
383796	23.2066	PierCami	12												12						
2493532	10.8564	MrtnRaab	13														19	15	13		
535836	22.0188	Jacobsen	13												19	13					
26250	33.3265	Jacobsen	13		41	39	13														
27480	32.8594	Jacobsen	13				17	13													
66816	30.9578	Jacobsen	13						13												
86934	29.9766	MJPC&JKA	13						23	18	16	13									
131574	28.5033	Jacobsen	13									39	13								
209912	28.1022	RobSmith	13										19	13							
1521800	16.7563	MrtnRaab	16														20	16			
2435476	10.6037	MrtnRaab	14														21	17	14		
834114	21.9588	M.Jansen	14												20	14					
11924	35.4550	Jacobsen	14	14																	
19170	34.6876	Jacobsen	14	26	15	14															
63524	32.7941	Jacobsen	14				18	14													
73200	30.1202	Jacobsen	14						21	16	14										
135182	28.5001	Jacobsen	14									40	14								
189570	28.0088	RobSmith	14										20	14							
538328	21.8527	M.Jansen	15												22	15					
30096	32.6764	Jacobsen	15				19	15													
82478	29.7727	Toni_Key	15						27	21	19	15									
173800	27.7067	Jacobsen	15										25	15							
1084830	21.8035	Rosnthal	16												23	16					
21126	34.6177	Jacobsen	16	29	17	16															
146856	28.3319	M.Jansen	16									45	16								
270602	27.7045	Rosnthal	16										27	16							
1069640	21.4978	Rosnthal	17												25	17					
22040	34.5159	Jacobsen	17	31	18	17															
101028	29.6477	RobSmith	17						31	23	21	17									
135232	28.1928	Jacobsen	17									48	17								
226278	27.6144	Jacobsen	17										29	17							
384902	22.3707	M.Jansen	17												17						
1471730	16.2111	MrtnRaab	18														22	18			
1045498	21.0130	Rosnthal	18												27	18					
37854	32.5151	Jacobsen	18				22	18													
77256	29.7857	Jacobsen	18						26	20	18										
258246	27.5751	Rosnthal	18										32	18							
324618	22.3122	M.Jansen	18												18						
1462522	16.1016	MrtnRaab	19														23	19			
818886	20.8333	M.Jansen	19												31	19					
10942	34.9114	Jacobsen	19	19																	
23812	34.2766	Jacobsen	19	40	20	19															
35960	32.4712	Jacobsen	19				23	19													
80774	29.4589	Jacobsen	19						35	27	24	19									
272586	27.5724	Rosnthal	19										33	19							
2055816	15.6743	PierCami	20														24	20			
12742	34.8525	Jacobsen	20	20																	
39408	32.4472	Jacobsen	20				24	20													
67370	30.3467	Jacobsen	20						20												
82640	29.4473	Jacobsen	20						36	28	25	20									
222854	27.5377	Toni_Key	20										34	20							
1004840	20.1968	Rosnthal	20												36	20					
1419558	15.6620	MrtnRaab	21														25	21			
22704	34.1509	Jacobsen	21	44	22	21															
91644	29.2970	Jacobsen	21						37	29	26	21									
128130	27.9402	MJPC&JKA	21										21								
213780	27.3088	RobSmith	21										35	21							
322982	21.8674	Toni_Key	21												21						
1004972	20.1966	Rosnthal	21												37	21					
1417014	15.6246	MrtnRaab	22														26	22			
23790	34.1236	Jacobsen	22	45	23	22															
36810	32.3930	Jacobsen	22				26	22													
104094	29.2142	MJPC&JKA	22						39	31	28	22									
143692	27.8323	MJPC&JKA	22										22								
228294	27.2609	Toni_Key	22										36	22							
865056	20.1598	PierCami	22												38	22					
1390164	15.3242	MrtnRaab	23														27	23			
11350	34.7489	Jacobsen	23	23																	
25408	34.0084	Jacobsen	23	48	24	23															
73294	29.5056	Jacobsen	23						33	25	23										
129220	27.8286	MJPC&JKA	23										23								
162762	27.2304	Jacobsen	23										37	23							
1002890	20.1556	Rosnthal	23												39	23					
1386416	15.3176	MrtnRaab	24														28	24			
22352	33.7498	Jacobsen	24		25	24															
46410	32.3200	Jacobsen	24				28	24													
66720	29.8466	Jacobsen	24						24												
80346	29.1252	Jacobsen	24						42	33	30	24									
155808	27.7981	Jacobsen	24										24								
250608	27.2170	Rosnthal	24										38	24							
338362	21.7854	RobSmith	24												24						
784246	20.0601	M.Jansen	24												42	24					
1575828	15.0964	M.Jansen	25														29	25			
13720	34.7057	Jacobsen	25	25																	
21300	33.7115	Jacobsen	25		26	25															
99868	29.0583	Jacobsen	25						43	34	31	25									
194460	27.1662	RobSmith	25										39	25							
997164	20.0410	Rosnthal	25												44	25					
1321710	14.6129	MrtnRaab	26														30	26			
50866	32.2207	Jacobsen	26				31	26													
71054	29.4620	Jacobsen	26						34	26											
90928	29.0154	MJPC&JKA	26						44	35	32	26									
125764	27.7064	Jacobsen	26										26								
225082	27.0851	Toni_Key	26										42	26							
365540	21.2069	RobSmith	26												26						
571948	20.0142	Jacobsen	26												45	26					
1452592	14.5724	RobSmith	27														31	27			
13704	34.6818	Jacobsen	27	27																	
25068	33.6132	Jacobsen	27		28	27															
30450	32.2155	Jacobsen	27				32	27													
72776	29.2839	Jacobsen	27						38	30	27										
85242	28.9713	Jacobsen	27						46	37	34	27									
167332	27.0564	Jacobsen	27										43	27							
540598	19.9971	M.Jansen	27												47	27					
1289448	14.2096	MrtnRaab	28														32	28			
22474	33.6102	Jacobsen	28		29	28															
37816	32.0958	Jacobsen	28				33	28													
70278	29.7625	Jacobsen	28						28												
79698	28.7625	MJPC&JKA	28							41	37	28									
126030	27.6148	Jacobsen	28										28								
170316	27.0345	Jacobsen	28										44	28							
360610	20.9216	RobSmith	28												28						
993888	19.9768	Rosnthal	28												49	28					
1289022	14.1924	MrtnRaab	29														33	29			
24412	33.6052	Jacobsen	29		30	29															
26592	32.2772	Jacobsen	29				29														
37786	32.0556	Jacobsen	29				34	29													
79578	28.7620	Toni_Key	29							42	38	29									
263574	27.0324	Rosnthal	29										45	29							
360054	20.8890	RobSmith	29												29						
809952	19.9443	M.Jansen	29												50	29					
1398354	13.3957	RobSmith	30														34	30			
12176	34.6060	Jacobsen	30	30																	
19332	33.6048	RobSmith	30		31	30															
39534	31.9988	Jacobsen	30				35	30													
66586	29.6835	Jacobsen	30						30												
109084	28.7413	Jacobsen	30							43	39	30									
128960	27.6038	Jacobsen	30										30								
263648	27.0229	Rosnthal	30										46	30							
326404	20.8574	M.Jansen	30												30						
809574	19.8675	M.Jansen	30													30					
2254930	11.2755	RosntlJA	31														35	31			
61578	31.9635	Toni_Key	31				36	31													
89692	28.6818	Jacobsen	31							44	40	31									
129532	27.5785	Toni_Key	31										31								
174864	26.9739	Toni_Key	31										47	31							
679690	19.7981	M.Jansen	31													31					
9030	34.5090	Jacobsen	32	32																	
25056	33.5059	Jacobsen	32		33	32															
35418	31.9591	Jacobsen	32				37	32													
254622	26.8202	Rosnthal	32										48	32							
358374	20.5309	M.Jansen	32												32						
875274	19.7343	PierCami	32													32					
2218822	7.1182	RobSmith	32														36	32			
14614	34.4755	Jacobsen	33	33																	
51942	31.8854	Jacobsen	33				38	33													
77514	29.0041	Jacobsen	33						45	36	33										
93570	28.6498	Jacobsen	33							46	42	33									
211044	26.7366	Jacobsen	33										50	33							
618480	19.7317	M.Jansen	33													33					
1569660	7.0001	M.Jansen	33														37	33			
18954	33.4915	Jacobsen	34		35	34															
40710	31.8627	Jacobsen	34				39	34													
96948	28.6249	Jacobsen	34							48	44	34									
246356	26.6965	Rosnthal	34											34							
318876	20.3669	M.Jansen	34												34						
843888	19.6665	PierCami	34													34					
2028240	6.5068	RobSmith	34														38	34			
11570	34.3835	Jacobsen	35	35																	
20004	33.4838	Jacobsen	35		36	35															
29804	31.8444	Jacobsen	35				40	35													
74980	28.9459	MJPC&JKA	35						47	38	35										
282702	26.6546	RobSmith	35											35							
342336	20.3206	Jacobsen	35												35						
967630	19.4470	Rosnthal	35													35					
13112	34.3477	Jacobsen	36	36																	
18508	33.4563	Jacobsen	36		37	36															
73722	28.8584	Jacobsen	36						48	39	36										
252708	26.6447	Rosnthal	36											36							
546518	19.4101	Jacobsen	36													36					
10924	34.3072	Jacobsen	37	37																	
22136	33.4436	Jacobsen	37		38	37															
37052	31.8213	Jacobsen	37				42	37													
89460	28.5636	Jacobsen	37								48	37									
181230	26.6431	Toni_Key	37											37							
830202	19.3475	PierCami	37													37					
12510	34.3038	Jacobsen	38	38																	
22364	33.4404	Jacobsen	38		39	38															
31146	31.8206	Jacobsen	38				43	38													
84234	28.5480	Jacobsen	38								49	38									
189604	26.4933	Toni_Key	38											38							
707970	19.3071	M.Jansen	38													38					
1284234	14.1659	MrtnRaab	39														39				
14028	34.2893	Jacobsen	39	39																	
176900	26.4883	Jacobsen	39											39							
960492	19.3044	Rosnthal	39													39					
1217460	13.4036	MrtnRaab	40														40				
17396	33.4121	Jacobsen	40		40																
23802	33.3047	Jacobsen	40		43	40															
38784	31.7367	Jacobsen	40				45	40													
71704	28.8164	MJPC&JKA	40							40											
131376	27.1415	RobSmith	40										40								
280566	26.4701	RobSmith	40											40							
360072	20.0760	RobSmith	40												40						
826800	19.2463	MJPC&JKA	40													40					
1212942	13.3981	MrtnRaab	41														41				
9370	34.2712	Jacobsen	41	41																	
21674	33.2910	Jacobsen	41		44	41															
33160	31.7327	Jacobsen	41				46	41													
70284	29.1308	Jacobsen	41						41												
140640	27.0857	Jacobsen	41										41								
251404	26.4034	Rosnthal	41											41							
333906	20.0698	RobSmith	41												41						
953940	19.1715	Rosnthal	41													41					
1216548	13.3919	MrtnRaab	42														42				
11868	34.2280	Jacobsen	42	42																	
17374	33.3091	Jacobsen	42		42																
25116	33.2776	M.Jansen	42		45	42															
62110	31.6880	Toni_Key	42				47	42													
97724	28.3876	Jacobsen	42									42									
237250	26.3139	Rosnthal	42											42							
622560	19.1515	M.Jansen	42													42					
1176666	12.9561	MrtnRaab	43														43				
21318	33.2557	Jacobsen	43		46	43															
44720	31.6591	Jacobsen	43				48	43													
73116	28.6311	Jacobsen	43							47	43										
93228	28.3660	Jacobsen	43									43									
440020	20.0600	Jacobsen	43												43						
756258	19.0704	M.Jansen	43													43					
1158992	12.7816	MrtnRaab	44														44				
34804	31.6366	Jacobsen	44				49	44													
101878	28.3555	MJPC&JKA	44									44									
159262	26.2755	Toni_Key	44											44							
571356	19.0057	M.Jansen	44													44					
1150108	12.6876	MrtnRaab	45														45				
22400	33.2046	Jacobsen	45		50	45															
33008	31.5838	Jacobsen	45				50	45													
212252	26.1934	Toni_Key	45											45							
856608	18.9608	PierCami	45													45					
1134502	12.5131	MrtnRaab	46														46				
11160	34.1091	Jacobsen	46	46																	
25888	33.1558	Jacobsen	46			46															
38118	31.5712	Jacobsen	46					46													
72954	28.5694	Jacobsen	46							50	46										
95312	28.3233	Jacobsen	46									46									
298728	26.1667	RobSmith	46											46							
312154	20.0025	Jacobsen	46												46						
942304	18.9389	Rosnthal	46													46					
1224222	12.2811	RobSmith	47														47				
10442	34.0379	Jacobsen	47	47																	
18180	33.2269	Jacobsen	47		47																
23116	33.1377	Jacobsen	47			47															
36920	31.5137	Jacobsen	47					47													
88530	28.3034	MJPC&JKA	47									47									
160330	26.1316	RobSmith	47											47							
788542	18.8448	M.Jansen	47													47					
1117820	11.2141	RobSmith	48														48				
20076	33.0978	Jacobsen	48			48															
54880	31.5118	RobSmith	48					48													
165604	26.1050	RobSmith	48											48							
316982	19.9865	RobSmith	48												48						
935950	18.8099	Rosnthal	48													48					
11382	33.9128	Jacobsen	49	49																	
17376	33.2151	Jacobsen	49		49																
62724	31.5065	Jacobsen	49					49													
69840	28.8561	Jacobsen	49						49												
154202	26.8129	Toni_Key	49										49								
210268	26.0915	RobSmith	49											49							
599040	18.7943	M.Jansen	49													49					
13782	33.8980	Jacobsen	50	50																	
68540	28.8546	Jacobsen	50						50												
75848	28.5089	Jacobsen	50								50										
93786	28.1763	Jacobsen	50									50									
174150	26.0706	RobSmith	50											50							
931870	18.7279	Rosnthal	50													50

Last fiddled with by robert44444uk on 2018-07-10 at 08:08
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