Prime p₀= 740704541399464529 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 16 2 130 2 58 2 16 2 (?)
a_n: 0 2 30 32 42 44 60 62 192 194 252 254 270 272
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: Theadalus
db: batch=73, k=14, 28 10 16 130 58 16

SPT(16)	740703642993350921	0 8 56 86 156 210 222 258 260 296 308 362 432 462 510 518	-898406113608
STPT(10)	740703721095916649	0 2 78 80 120 122 162 164 240 242	-820303547880
STPT(10)	740703779165649251	0 2 30 32 120 122 210 212 240 242	-762233815278
STPT(10)	740703955026584537	0 2 72 74 102 104 132 134 204 206	-586372879992
SPT(16)	740704413552885179	0 2 30 68 72 80 84 98 114 128 132 140 144 182 210 212	-127846579350
SPT(16)	740704438620230863	0 4 16 36 100 174 184 246 268 330 340 414 478 498 510 514	-102779233666
SPT(16)	740704759421555837	0 2 20 42 72 90 104 122 132 150 164 182 212 234 252 254	218022091308
STPT(10)	740704759931956991	0 2 78 80 108 110 138 140 216 218	218532492462
SPT(16)	740704948441556767	0 12 22 34 70 100 120 126 160 166 186 216 252 264 274 286	407042092238
STPT(10)	740705008937528651	0 2 30 32 78 80 126 128 156 158	467538064122
SPT(16)	740705069211939787	0 36 46 72 90 106 186 300 322 436 516 532 550 576 586 622	527812475258