Prime p₀= 1237157953265782967 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 70 2 58 2 88 2 154 2 40 2 (?)
a_n: 0 2 12 14 84 86 144 146 234 236 390 392 432 434
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: 434
Found by: Cruncher Pete
db: batch=77, k=14, 10 70 58 88 154 40

STPT(10)	1237156914468507467	0 2 30 32 42 44 54 56 84 86	-1038797275500
STPT(10)	1237157007386880257	0 2 30 32 42 44 54 56 84 86	-945878902710
SPT(20)	1237157058143748949	0 22 48 54 64 78 82 132 138 238 294 394 400 450 454 468 478 484 510 532	-895122034018
SPT(16)	1237157284670886563	0 36 54 56 80 90 96 140 144 188 194 204 228 230 248 284	-668594896404
STPT(10)	1237157365754490767	0 2 30 32 72 74 114 116 144 146	-587511292200
TPT(14)	1237157689784219807	0 2 30 32 42 44 60 62 84 86 90 92 114 116	-263481563160
SPT(18)	1237158164569201241	0 6 12 38 42 90 96 122 126 152 156 182 188 236 240 266 272 278	211303418274
SPT(16)	1237158212803105139	0 2 8 32 42 44 134 170 192 228 318 320 330 354 360 362	259537322172
SPT(16)	1237158509526572639	0 18 74 84 122 140 182 188 354 360 402 420 458 468 524 542	556260789672
TPT(14)	1237158693001309031	0 2 90 92 120 122 126 128 186 188 258 260 336 338	739735526064
SPT(16)	1237158985125135517	0 82 90 102 124 142 154 190 306 342 354 372 394 406 414 496	1031859352550