Prime p₀= 1122864341673910349 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 46 2 46 2 52 2 28 2 28 2 (?)
a_n: 0 2 42 44 90 92 138 140 192 194 222 224 252 254
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: 254
Found by: crashtech
db: batch=76, k=14, 40 46 46 52 28 28

STPT(10)	1122863697162449027	0 2 30 32 60 62 90 92 120 122	-644511461322
STPT(10)	1122863854542440081	0 2 36 38 78 80 120 122 156 158	-487131470268
SPT(16)	1122863874295949837	0 6 32 62 74 102 116 120 146 150 164 192 204 234 260 266	-467377960512
SPT(16)	1122863919023324171	0 36 66 128 150 162 168 176 192 200 206 218 240 302 332 368	-422650586178
SPT(16)	1122864162589760407	0 4 6 12 42 144 172 174 202 204 232 334 364 370 372 376	-179084149942
SPT(16)	1122864262582036529	0 14 24 44 74 92 98 102 140 144 150 168 198 218 228 242	-79091873820
SPT(16)	1122864449155939757	0 12 42 50 54 56 92 116 120 144 180 182 186 194 224 236	107482029408
SPT(16)	1122864460653037387	0 22 64 76 82 94 96 120 136 160 162 174 180 192 234 256	118979127038
SPT(16)	1122864621014008447	0 12 66 94 102 150 172 196 210 234 256 304 312 340 394 406	279340098098
STPT(10)	1122864624980215847	0 2 30 32 72 74 114 116 144 146	283306305498
SPT(16)	1122864648802965317	0 6 14 30 44 54 90 96 104 110 146 156 170 186 194 200	307129054968