Prime p₀= 1265644597998643787 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 58 2 40 2 106 2 40 2 124 2 (?)
a_n: 0 2 12 14 72 74 114 116 222 224 264 266 390 392
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 392
Found by: Theadalus
db: batch=77, k=14, 10 58 40 106 40 124

SPT(13)	1265643059912620673	0 6 60 96 126 180 198 216 270 300 336 390 396	-1538086023114
STPT(10)	1265644022397815297	0 2 30 32 42 44 54 56 84 86	-575600828490
STPT(10)	1265644154686036421	0 2 6 8 18 20 30 32 36 38	-443312607366
SPT(13)	1265644382720960729	0 48 78 84 114 120 144 168 174 204 210 240 288	-215277683058
STPT(10)	1265644466382765611	0 2 6 8 18 20 30 32 36 38	-131615878176
SPT(16)	1265644529325559853	0 56 66 86 114 144 186 194 210 218 260 290 318 338 348 404	-68673083934
SPT(16)	1265645461315810987	0 34 42 46 60 66 90 112 234 256 280 286 300 304 312 346	863317167200
TPT(14)	1265645582167758287	0 2 12 14 72 74 114 116 150 152 222 224 234 236	984169114500
SPT(16)	1265645756544689209	0 34 40 70 100 114 130 232 390 492 508 522 552 582 588 622	1158546045422
SPT(20)	1265645762913606121	0 10 12 40 42 48 66 88 126 130 258 262 300 322 340 346 348 376 378 388	1164914962334
SPT(16)	1265646047003634749	0 8 32 38 74 110 122 140 162 180 192 228 264 270 294 302	1449004990962