Prime p₀= 2437472088290318159 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 112 2 16 2 88 2 28 2 16 2 (?)
a_n: 0 2 78 80 192 194 210 212 300 302 330 332 348 350
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: 350
Found by: JonS
db: batch=82, k=14, 76 112 16 88 28 16

SPT(16)	2437470727878999937	0 4 22 36 60 66 112 124 132 144 190 196 220 234 252 256	-1360411318222
SPT(16)	2437470969435706889	0 24 38 68 104 180 192 254 378 440 452 528 564 594 608 632	-1118854611270
STPT(10)	2437471079269108691	0 2 6 8 48 50 90 92 96 98	-1009021209468
STPT(10)	2437471138218792881	0 2 6 8 18 20 30 32 36 38	-950071525278
SPT(16)	2437471905819940651	0 18 48 60 82 132 138 142 156 160 166 216 238 250 280 298	-182470377508
SPT(16)	2437472019811411441	0 6 96 112 136 138 148 162 166 180 190 192 216 232 322 328	-68478906718
SPT(16)	2437472224177186123	0 16 28 70 78 126 180 204 250 274 328 376 384 426 438 454	135886867964
STPT(10)	2437472670002370347	0 2 12 14 42 44 72 74 84 86	581712052188
SPT(20)	2437473204338263363	0 10 16 48 60 130 138 184 264 298 306 340 420 466 474 544 556 588 594 604	1116047945204
STPT(10)	2437473265587735671	0 2 6 8 18 20 30 32 36 38	1177297417512
SPT(18)	2437473430483434169	0 58 124 142 154 184 222 232 234 268 270 280 318 348 360 378 444 502	1342193116010