Prime p₀= 2506379379391224317 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 22 2 58 2 64 2 10 2 16 2 (?)
a_n: 0 2 30 32 54 56 114 116 180 182 192 194 210 212
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: 212
Found by: Ben
db: batch=82, k=14, 28 22 58 64 10 16

SPT(16)	2506377390606297721	0 16 18 52 60 118 132 156 232 256 270 328 336 370 372 388	-1988784926596
STPT(10)	2506377707389231769	0 2 42 44 60 62 78 80 120 122	-1672001992548
STPT(10)	2506378164823150757	0 2 42 44 72 74 102 104 144 146	-1214568073560
SPT(16)	2506378472063080193	0 20 60 104 134 174 194 204 206 216 236 276 306 350 390 410	-907328144124
TPT(14)	2506378604703011999	0 2 42 44 102 104 132 134 210 212 228 230 240 242	-774688212318
STPT(10)	2506379027325864797	0 2 30 32 120 122 210 212 240 242	-352065359520
SPT(16)	2506379384376818917	0 36 46 82 102 114 120 186 250 316 322 334 354 390 400 436	4985594600
SPT(16)	2506379459762368409	0 8 20 60 102 104 108 140 192 224 228 230 272 312 324 332	80371144092
SPT(16)	2506379923100646793	0 6 16 84 88 90 96 100 144 148 154 156 160 228 238 244	543709422476
SPT(16)	2506380245460928691	0 8 32 92 110 152 158 228 320 390 396 438 456 516 540 548	866069704374
SPT(16)	2506380508958421269	0 12 18 32 42 54 108 144 278 314 368 380 390 404 410 422	1129567196952