Prime p₀= 728622388409456039 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 40 2 136 2 58 2 76 2 88 2 (?)
a_n: 0 2 90 92 132 134 270 272 330 332 408 410 498 500
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: 500
Found by: crashtech
db: batch=73, k=14, 88 40 136 58 76 88

SPT(16)	728621688176034833	0 8 20 38 66 96 110 116 168 174 188 218 246 264 276 284	-700233421206
SPT(16)	728621772288799663	0 40 106 150 154 178 264 268 456 460 546 570 574 618 684 724	-616120656376
SPT(16)	728622094095818831	0 18 20 42 56 72 98 156 182 240 266 282 296 318 320 338	-294313637208
SPT(16)	728622159023125769	0 54 84 114 168 254 260 264 278 282 288 374 428 458 488 542	-229386330270
STPT(10)	728622229644345989	0 2 42 44 120 122 198 200 240 242	-158765110050
SPT(16)	728622317513860153	0 24 48 54 76 88 96 124 180 208 216 228 250 256 280 304	-70895595886
STPT(10)	728622545949154457	0 2 42 44 72 74 102 104 144 146	157539698418
SPT(16)	728622600773172257	0 14 26 50 96 110 116 120 140 144 150 164 210 234 246 260	212363716218
SPT(16)	728622913068367399	0 34 60 78 102 162 168 174 208 214 220 280 304 322 348 382	524658911360
TPT(14)	728623489466469899	0 2 12 14 78 80 150 152 168 170 222 224 318 320	1101057013860
TPT(14)	728623716752315411	0 2 186 188 228 230 276 278 318 320 390 392 408 410	1328342859372