Prime p₀= 2507386947426585839 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 136 2 28 2 22 2 4 2 70 2 40 2 (?)
a_n: 0 2 138 140 168 170 192 194 198 200 270 272 312 314
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: 314
Found by: [AF>Linux]Rogue 9
db: batch=82, k=14, 136 28 22 4 70 40

SPT(16)	2507384913151824721	0 30 46 66 72 100 112 130 192 210 222 250 256 276 292 322	-2034274761118
STPT(10)	2507385437365321769	0 2 12 14 90 92 168 170 180 182	-1510061264070
SPT(16)	2507385623607048551	0 38 48 66 110 146 162 168 230 236 252 288 332 350 360 398	-1323819537288
SPT(16)	2507386285485349189	0 12 22 28 78 108 132 150 190 208 232 262 312 318 328 340	-661941236650
STPT(10)	2507386652967588941	0 2 6 8 48 50 90 92 96 98	-294458996898
SPT(20)	2507386854911557741	0 28 36 58 72 82 136 198 262 282 286 306 370 432 486 496 510 532 540 568	-92515028098
SPT(16)	2507387252282918527	0 22 34 36 64 100 112 114 172 174 186 222 250 252 264 286	304856332688
SPT(16)	2507387566958870311	0 18 66 102 106 108 130 148 240 258 280 282 286 322 370 388	619532284472
STPT(10)	2507388185310799337	0 2 30 32 42 44 54 56 84 86	1237884213498
SPT(16)	2507388382311451519	0 24 34 48 60 82 88 108 154 174 180 202 214 228 238 262	1434884865680
STPT(10)	2507388857276423927	0 2 42 44 72 74 102 104 144 146	1909849838088