Prime p₀= 2788042771154891639 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 22 2 58 2 4 2 70 2 40 2 (?)
a_n: 0 2 48 50 72 74 132 134 138 140 210 212 252 254
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: [SG]ATA-Rolf
db: batch=82, k=14, 46 22 58 4 70 40

SPT(16)	2788040986065689143	0 34 70 76 100 130 154 184 186 216 240 270 294 300 336 370	-1785089202496
SPT(16)	2788041465310797611	0 2 26 60 68 86 146 152 216 222 282 300 308 342 366 368	-1305844094028
SPT(16)	2788041609553205437	0 70 76 102 126 130 144 172 234 262 276 280 304 330 336 406	-1161601686202
SPT(16)	2788041703608042781	0 6 58 60 78 100 118 126 160 168 186 208 226 228 280 286	-1067546848858
TPT(16)	2788041723522907427	0 2 30 32 42 44 120 122 132 134 144 146 294 296 300 302	-1047631984212
SPT(16)	2788042163930343997	0 34 46 84 106 130 174 190 216 232 276 300 322 360 372 406	-607224547642
STPT(10)	2788042841148634637	0 2 12 14 42 44 72 74 84 86	69993742998
SPT(16)	2788043213649111401	0 8 18 60 68 120 168 176 180 188 236 288 296 338 348 356	442494219762
STPT(10)	2788043895760761887	0 2 30 32 42 44 54 56 84 86	1124605870248
SPT(16)	2788044562628414183	0 20 50 84 108 164 168 180 248 260 264 320 344 378 408 428	1791473522544
STPT(10)	2788044749859246971	0 2 30 32 60 62 90 92 120 122	1978704355332