Prime p₀= 2562111814787875277 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 34 2 88 2 28 2 52 2 34 2 (?)
a_n: 0 2 54 56 90 92 180 182 210 212 264 266 300 302
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: 302
Found by: Penguin
db: batch=82, k=14, 52 34 88 28 52 34

SPT(16)	2562110349564458321	0 30 68 72 80 110 126 128 210 212 228 258 266 270 308 338	-1465223416956
STPT(10)	2562110956780341467	0 2 54 56 72 74 90 92 144 146	-858007533810
SPT(16)	2562111276625950611	0 42 72 86 90 212 216 240 308 332 336 458 462 476 506 548	-538161924666
SPT(16)	2562111303185794219	0 10 60 82 142 150 198 228 304 334 382 390 450 472 522 532	-511602081058
STPT(10)	2562111563223635231	0 2 6 8 48 50 90 92 96 98	-251564240046
SPT(16)	2562111686741587823	0 20 24 30 98 104 126 138 266 278 300 306 374 380 384 404	-128046287454
STPT(12)	2562111832704621479	0 2 18 20 42 44 78 80 102 104 120 122	17916746202
TPT(14)	2562112546764393437	0 2 84 86 150 152 180 182 204 206 222 224 300 302	731976518160
SPT(16)	2562112627736682547	0 70 94 114 120 132 142 202 354 414 424 436 442 462 486 556	812948807270
TPT(14)	2562112765203482549	0 2 42 44 60 62 210 212 282 284 288 290 378 380	950415607272
STPT(10)	2562113271252684971	0 2 6 8 48 50 90 92 96 98	1456464809694