Prime p₀= 1122887998332961961 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 40 2 76 2 58 2 22 2 4 2 (?)
a_n: 0 2 36 38 78 80 156 158 216 218 240 242 246 248
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: 248
Found by: crashtech
db: batch=76, k=14, 34 40 76 58 22 4

SPT(16)	1122886427173109693	0 6 8 48 54 90 108 120 194 206 224 260 266 306 308 314	-1571159852268
SPT(16)	1122886496051702101	0 16 18 70 100 126 166 196 252 282 322 348 378 430 432 448	-1502281259860
STPT(10)	1122886816741309559	0 2 18 20 60 62 102 104 120 122	-1181591652402
SPT(16)	1122887417501578039	0 28 54 100 124 174 190 210 232 252 268 318 342 388 414 442	-580831383922
STPT(10)	1122887556625957919	0 2 18 20 30 32 42 44 60 62	-441707004042
SPT(16)	1122887738223602591	0 8 48 62 132 162 192 218 300 326 356 386 456 470 510 518	-260109359370
STPT(10)	1122888531453682517	0 2 30 32 42 44 54 56 84 86	533120720556
SPT(18)	1122888565454481391	0 12 30 40 76 90 96 100 102 166 168 172 178 192 228 238 256 268	567121519430
SPT(16)	1122888801246705529	0 84 102 124 144 180 204 220 222 238 262 298 318 340 358 442	802913743568
SPT(16)	1122889151101892659	0 58 70 72 94 144 162 168 214 220 238 288 310 312 324 382	1152768930698
STPT(10)	1122889326273399257	0 2 60 62 72 74 84 86 144 146	1327940437296