Prime p₀= 1270492949211887507 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 40 2 28 2 388 2 28 2 34 2 (?)
a_n: 0 2 12 14 54 56 84 86 474 476 504 506 540 542
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: 542
Found by: Megacruncher
db: batch=77, k=14, 10 40 28 388 28 34

SPT(16)	1270491636216759287	0 50 62 116 140 162 206 216 470 480 524 546 570 624 636 686	-1312995128220
SPT(16)	1270491782040126577	0 12 94 96 114 150 172 180 196 204 226 262 280 282 364 376	-1167171760930
STPT(10)	1270492043269911767	0 2 30 32 42 44 54 56 84 86	-905941975740
STPT(10)	1270492101546435809	0 2 18 20 30 32 42 44 60 62	-847665451698
SPT(16)	1270492868559784229	0 8 38 62 132 138 180 194 318 332 374 380 450 474 504 512	-80652103278
SPT(16)	1270492888433906897	0 42 56 104 174 212 236 356 390 510 534 572 642 690 704 746	-60777980610
SPT(16)	1270493002016581351	0 16 40 42 46 52 60 112 126 178 186 192 196 198 222 238	52804693844
TPT(14)	1270493057329538969	0 2 78 80 90 92 108 110 120 122 258 260 348 350	108117651462
SPT(16)	1270493189248001989	0 18 34 48 64 72 88 90 112 114 130 138 154 168 184 202	240036114482
STPT(10)	1270493306563806737	0 2 24 26 42 44 60 62 84 86	357351919230
SPT(16)	1270493614347343643	0 14 20 38 50 60 200 270 308 378 518 528 540 558 564 578	665135456136