Prime p₀= 740872775196657281 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 10 2 88 2 28 2 166 2 22 2 (?)
a_n: 0 2 36 38 48 50 138 140 168 170 336 338 360 362
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: 362
Found by: Theadalus
db: batch=73, k=14, 34 10 88 28 166 22

SPT(16)	740871464005688707	0 4 30 42 72 84 96 124 132 160 172 184 214 226 252 256	-1311190968574
SPT(16)	740871784281609949	0 24 30 94 112 138 148 184 258 294 304 330 348 412 418 442	-990915047332
STPT(10)	740871996092208509	0 2 12 14 90 92 168 170 180 182	-779104448772
SPT(16)	740872152353732857	0 6 22 34 72 76 90 96 100 106 120 124 162 174 190 196	-622842924424
TPT(14)	740872380300085331	0 2 6 8 48 50 60 62 126 128 156 158 210 212	-394896571950
SPT(16)	740872509493555303	0 28 76 100 126 168 184 190 294 300 316 358 384 408 456 484	-265703101978
SPT(18)	740872824688696649	0 108 120 122 200 210 222 278 302 318 342 398 410 420 498 500 512 620	49492039368
STPT(10)	740872965414725279	0 2 42 44 90 92 138 140 180 182	190218067998
STPT(10)	740873599260167081	0 2 36 38 78 80 120 122 156 158	824063509800
STPT(10)	740873848910491757	0 2 24 26 42 44 60 62 84 86	1073713834476
STPT(12)	740873997617805047	0 2 12 14 42 44 162 164 192 194 204 206	1222421147766