Prime p₀= 2356697515809235607 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 112 2 76 2 46 2 40 2 118 2 58 2 (?)
a_n: 0 2 114 116 192 194 240 242 282 284 402 404 462 464
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: 464
Found by: Landjunge
db: batch=81, k=14, 112 76 46 40 118 58

STPT(10)	2356695639925775129	0 2 42 44 60 62 78 80 120 122	-1875883460478
SPT(16)	2356695742717176137	0 30 32 84 90 102 104 182 342 420 422 434 440 492 494 524	-1773092059470
SPT(16)	2356696427724873151	0 10 12 36 40 46 88 100 108 120 162 168 172 196 198 208	-1088084362456
SPT(16)	2356696466774184133	0 48 60 88 118 130 166 180 316 330 366 378 408 436 448 496	-1049035051474
STPT(12)	2356696929004271801	0 2 6 8 48 50 78 80 120 122 126 128	-586804963806
SPT(16)	2356696954455194161	0 12 46 72 76 88 96 118 180 202 210 222 226 252 286 298	-561354041446
SPT(16)	2356697738179534693	0 16 66 100 118 130 180 196 198 214 264 276 294 328 378 394	222370299086
STPT(10)	2356698025245913211	0 2 36 38 78 80 120 122 156 158	509436677604
SPT(16)	2356698083273903843	0 14 18 48 60 146 168 200 234 266 288 374 386 416 420 434	567464668236
STPT(10)	2356698349091400071	0 2 6 8 18 20 30 32 36 38	833282164464
SPT(16)	2356698475672274509	0 52 54 100 112 124 130 168 184 222 228 240 252 298 300 352	959863038902