Prime p₀= 2310441878799122441 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 34 2 88 2 10 2 106 2 58 2 (?)
a_n: 0 2 90 92 126 128 216 218 228 230 336 338 396 398
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: 398
Found by: FritzB
db: batch=81, k=14, 88 34 88 10 106 58

SPT(16)	2310440663889849779	0 14 38 44 84 140 320 354 374 408 588 644 684 690 714 728	-1214909272662
SPT(16)	2310440879849973041	0 42 72 78 108 122 140 162 176 198 216 230 260 266 296 338	-998949149400
TPT(14)	2310441215394856781	0 2 30 32 180 182 186 188 210 212 276 278 318 320	-663404265660
SPT(16)	2310441323803709839	0 30 40 42 72 108 120 198 304 382 394 430 460 462 472 502	-554995412602
STPT(10)	2310441451558910639	0 2 12 14 30 32 48 50 60 62	-427240211802
SPT(16)	2310441811132304191	0 18 60 90 108 112 138 150 160 172 198 202 220 250 292 310	-67666818250
SPT(16)	2310442836093174787	0 34 36 96 112 132 190 222 274 306 364 384 400 460 462 496	957294052346
SPT(16)	2310442884296125079	0 18 44 62 72 78 120 132 140 152 194 200 210 228 254 272	1005497002638
SPT(16)	2310443643580746137	0 14 32 50 84 140 162 192 302 332 354 410 444 462 480 494	1764781623696
STPT(10)	2310443812487212247	0 2 24 26 42 44 60 62 84 86	1933688089806
SPT(16)	2310443900469401101	0 6 18 42 48 58 88 126 172 210 240 250 256 280 292 298	2021670278660