Prime p₀= 2297885500828399127 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 10 2 4 2 82 2 136 2 58 2 (?)
a_n: 0 2 72 74 84 86 90 92 174 176 312 314 372 374
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: 374
Found by: Landjunge
db: batch=81, k=14, 70 10 4 82 136 58

SPT(16)	2297883410236081249	0 10 28 40 52 88 102 124 168 190 204 240 252 264 282 292	-2090592317878
SPT(16)	2297883621594057577	0 10 34 42 64 82 112 136 150 174 204 222 244 252 276 286	-1879234341550
STPT(10)	2297885076107423861	0 2 36 38 78 80 120 122 156 158	-424720975266
SPT(16)	2297885127483094217	0 50 74 102 120 126 132 146 180 194 200 206 224 252 276 326	-373345304910
SPT(16)	2297885307766008187	0 10 42 162 232 250 276 316 366 406 432 450 520 640 672 682	-193062390940
STPT(10)	2297885379252771569	0 2 42 44 120 122 198 200 240 242	-121575627558
TPT(14)	2297886082075619177	0 2 60 62 102 104 162 164 204 206 312 314 354 356	581247220050
SPT(16)	2297886320572164527	0 20 32 50 80 132 156 164 252 260 284 336 366 384 396 416	819743765400
STPT(10)	2297886446955377417	0 2 42 44 72 74 102 104 144 146	946126978290
SPT(16)	2297886640238549029	0 24 42 52 70 82 90 94 108 112 120 132 150 160 178 202	1139410149902
SPT(16)	2297886971991122731	0 16 46 60 76 162 190 192 280 282 310 396 412 426 456 472	1471162723604