Prime p₀= 1231521125089109537 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 82 2 34 2 58 2 40 2 40 2 (?)
a_n: 0 2 90 92 174 176 210 212 270 272 312 314 354 356
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: 356
Found by: Megacruncher
db: batch=77, k=14, 88 82 34 58 40 40

SPT(16)	1231520656822914961	0 18 40 46 48 72 90 96 172 178 196 220 222 228 250 268	-468266194576
STPT(10)	1231520913035908667	0 2 12 14 72 74 132 134 144 146	-212053200870
STPT(10)	1231520916446480741	0 2 6 8 48 50 90 92 96 98	-208642628796
STPT(10)	1231520953019494589	0 2 12 14 90 92 168 170 180 182	-172069614948
SPT(16)	1231520969076538961	0 38 56 62 86 120 150 228 230 308 338 372 396 402 420 458	-156012570576
STPT(10)	1231521023770852817	0 2 30 32 60 62 90 92 120 122	-101318256720
STPT(10)	1231521172944573521	0 2 6 8 48 50 90 92 96 98	47855463984
TPT(14)	1231521177517521167	0 2 90 92 102 104 114 116 132 134 144 146 180 182	52428411630
SPT(16)	1231521472314087323	0 14 50 74 80 84 110 116 144 150 176 180 186 210 246 260	347224977786
SPT(16)	1231521677925991063	0 10 94 124 154 184 190 196 288 294 300 330 360 390 474 484	552836881526
STPT(10)	1231521696086965469	0 2 18 20 30 32 42 44 60 62	570997855932