Prime p₀= 2564365978876048811 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 40 2 76 2 40 2 28 2 70 2 (?)
a_n: 0 2 6 8 48 50 126 128 168 170 198 200 270 272
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: 272
Found by: RFGuy_KCCO
db: batch=82, k=14, 4 40 76 40 28 70

SPT(16)	2564364100675158101	0 8 12 140 176 192 218 302 306 390 416 432 468 596 600 608	-1878200890710
TPT(14)	2564364278084658617	0 2 12 14 42 44 120 122 192 194 234 236 294 296	-1700791390194
SPT(16)	2564364583708208173	0 18 40 48 106 156 198 204 250 256 298 348 406 414 436 454	-1395167840638
SPT(16)	2564364964447844191	0 6 96 118 132 138 142 156 292 306 310 316 330 352 442 448	-1014428204620
STPT(10)	2564364988075338827	0 2 30 32 42 44 54 56 84 86	-990800709984
SPT(16)	2564365815725878517	0 42 90 134 162 246 260 266 300 306 320 404 432 476 524 566	-163150170294
SPT(16)	2564366174619384389	0 2 24 60 62 80 104 122 150 168 192 210 212 248 270 272	195743335578
SPT(16)	2564366757246083567	0 26 30 50 60 74 120 156 164 200 246 260 270 290 294 320	778370034756
SPT(16)	2564366792518227731	0 26 60 66 102 110 126 150 158 182 198 206 242 248 282 308	813642178920
SPT(16)	2564366950195810057	0 34 36 60 114 156 166 180 190 204 214 256 310 334 336 370	971319761246
STPT(10)	2564366954792704811	0 2 36 38 78 80 120 122 156 158	975916656000