Prime p₀= 1025669356732441961 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 28 2 58 2 28 2 10 2 28 2 (?)
a_n: 0 2 36 38 66 68 126 128 156 158 168 170 198 200
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: 200
Found by: stoneageman
db: batch=76, k=14, 34 28 58 28 10 28

SPT(16)	1025667960873383489	0 50 54 78 110 128 168 182 210 224 264 282 314 338 342 392	-1395859058472
STPT(10)	1025667963858418589	0 2 42 44 60 62 78 80 120 122	-1392874023372
SPT(16)	1025668377638758171	0 10 28 70 90 112 118 132 178 192 198 220 240 282 300 310	-979093683790
SPT(16)	1025668444192785331	0 22 30 42 136 180 210 232 396 418 448 492 586 598 606 628	-912539656630
SPT(16)	1025668520572049477	0 26 30 32 60 102 110 114 182 186 194 236 264 266 270 296	-836160392484
SPT(16)	1025668779462475717	0 70 106 114 142 156 184 252 304 372 400 414 442 450 486 556	-577269966244
TPT(16)	1025669892911831939	0 2 48 50 72 74 132 134 168 170 210 212 258 260 300 302	536179389978
SPT(16)	1025669894196643039	0 4 18 60 114 130 192 232 270 310 372 388 442 484 498 502	537464201078
SPT(16)	1025669995389466837	0 42 46 60 142 196 210 222 274 286 300 354 436 450 454 496	638657024876
STPT(10)	1025670081206746979	0 2 12 14 90 92 168 170 180 182	724474305018
STPT(10)	1025670212207218841	0 2 6 8 48 50 90 92 96 98	855474776880