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Old 2018-05-15, 00:40   #8
ATH
Einyen
 
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Dec 2003
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For the known big prime gaps GSC is only above 0.8 below 2^64 and it gets smaller and smaller with bigger primes even if those gaps have merit above 35, and it is really tiny for the largest gaps.

Any new big gap above 2^64 with GSC above 0.8 or even 0.5 would be something new.

Code:
Gn	Pn			Merit		Gn/(ln(Pn)^2)	Ford-Green-Konyagin-Maynard-Tao
5103138	7.69542115*10^216848	10.22031845	0.00002047	 	 2.12060937
6582144	8.46506984*10^216840	13.18288411	0.00002640	 	 2.73531863
4680156	5.10477651*10^99749	20.37666041	0.00008872		 4.50159088
66520	3.29280820*10^815	35.42445941	0.01886489		13.50196237
26892	4.69622677*10^320	36.42056789	0.04932537		16.38392439
26054	5.88832005*10^305	37.00529401	0.05255975		16.80505451
18306	7.04109715*10^208	38.06696007	0.07915948		18.72974074
15900	1.93693327*10^174	39.62015365	0.09872683		20.31243105
13692	3.25418593*10^162	36.59018324	0.09778276		19.07131098
10716	1.83937772*10^126	36.85828850	0.12677617		20.45427745
8382	1.74442287*10^96	37.82412584	0.17068295		22.59742318
8350	2.93703234*10^86	41.93878373	0.21064211		25.84973884
1510	6787988999657777797	34.82336886	0.80309074		43.33266457
1454	3219107182492871783	34.11893253	0.80062005		43.03407437
1476	1425172824437699411	35.31030807	0.84472754		45.22507308
1442	804212830686677669	34.97568651	0.84833471		45.29864017
1370	418032645936712127	33.76518602	0.83218087		44.30979390
1132	1693182318746371	32.28254764	0.92063859		48.34468117

Ford-Green-Konyagin-Maynard-Tao:

        log X * loglog X * loglogloglog X
G(X) >  ---------------------------------
                  logloglog X
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