Prime p₀= 957074810714495969 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 106 2 40 2 28 2 28 2 (?)
a_n: 0 2 42 44 60 62 168 170 210 212 240 242 270 272
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: 272
Found by: stoneageman
db: batch=76, k=14, 40 16 106 40 28 28

SPT(16)	957073433197232641	0 6 16 36 52 66 70 72 76 78 82 96 112 132 142 148	-1377517263328
TPT(14)	957073478459586281	0 2 6 8 120 122 138 140 210 212 288 290 330 332	-1332254909688
SPT(16)	957073793111595077	0 24 62 86 90 140 156 174 182 200 216 266 270 294 332 356	-1017602900892
STPT(10)	957073804497765971	0 2 30 32 78 80 126 128 156 158	-1006216729998
STPT(10)	957074211428923967	0 2 30 32 42 44 54 56 84 86	-599285572002
SPT(16)	957074753824360729	0 10 48 160 178 238 258 270 280 292 312 372 390 502 540 550	-56890135240
STPT(10)	957074816162016161	0 2 30 32 78 80 126 128 156 158	5447520192
SPT(16)	957074907157519651	0 46 88 90 132 166 246 288 340 382 462 496 538 540 582 628	96443023682
STPT(10)	957075317451769457	0 2 30 32 42 44 54 56 84 86	506737273488
SPT(16)	957075322847253419	0 24 38 62 84 122 228 300 302 374 480 518 540 564 578 602	512132757450
STPT(10)	957075417341013557	0 2 30 32 72 74 114 116 144 146	606626517588