Prime p₀= 1042290215374029239 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 10 2 76 2 40 2 16 2 22 2 (?)
a_n: 0 2 78 80 90 92 168 170 210 212 228 230 252 254
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: 254
Found by: stoneageman
db: batch=76, k=14, 76 10 76 40 16 22

SPT(16)	1042287908606327623	0 114 126 130 154 160 184 214 216 246 270 276 300 304 316 430	-2306767701616
STPT(10)	1042287940913570837	0 2 54 56 132 134 210 212 264 266	-2274460458402
SPT(16)	1042288573783074509	0 12 62 78 92 182 192 210 272 290 300 390 404 420 470 482	-1641590954730
STPT(12)	1042289172165394169	0 2 18 20 42 44 78 80 102 104 120 122	-1043208635070
SPT(16)	1042289325376922041	0 18 40 48 58 70 72 112 156 196 198 210 220 228 250 268	-889997107198
TPT(14)	1042289863283060129	0 2 12 14 78 80 168 170 288 290 348 350 390 392	-352090969110
STPT(10)	1042290273687408209	0 2 48 50 60 62 72 74 120 122	58313378970
STPT(10)	1042290339154481111	0 2 36 38 78 80 120 122 156 158	123780451872
SPT(16)	1042290438675950239	0 24 34 70 84 100 114 178 360 424 438 454 468 504 514 538	223301921000
SPT(16)	1042290672688275079	0 24 54 72 94 138 144 172 180 208 214 258 280 298 328 352	457314245840
SPT(16)	1042290717657850669	0 28 72 78 82 84 112 120 172 180 208 210 214 220 264 292	502283821430