Prime p₀= 1427297638960266581 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 88 2 88 2 10 2 136 2 40 2 (?)
a_n: 0 2 6 8 96 98 186 188 198 200 336 338 378 380
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: 380
Found by: MarkRBright
db: batch=78, k=14, 4 88 88 10 136 40

TPT(14)	1427297017230437699	0 2 78 80 90 92 162 164 288 290 300 302 342 344	-621729828882
SPT(16)	1427297034392578463	0 8 20 24 30 38 56 74 90 108 126 134 140 144 156 164	-604567688118
STPT(10)	1427297077172085011	0 2 6 8 48 50 90 92 96 98	-561788181570
SPT(16)	1427297227244065757	0 24 60 164 170 222 284 306 380 402 464 516 522 626 662 686	-411716200824
SPT(16)	1427297232085883033	0 14 38 74 80 96 116 168 176 228 248 264 270 306 330 344	-406874383548
SPT(16)	1427297487973052303	0 18 38 44 60 86 98 110 144 156 168 194 210 216 236 254	-150987214278
STPT(10)	1427298041818824191	0 2 30 32 78 80 126 128 156 158	402858557610
STPT(10)	1427298563339776817	0 2 30 32 42 44 54 56 84 86	924379510236
TPT(14)	1427298567488977151	0 2 90 92 180 182 210 212 216 218 276 278 288 290	928528710570
STPT(10)	1427298655407882539	0 2 18 20 60 62 102 104 120 122	1016447615958
SPT(16)	1427298665416033577	0 14 30 110 114 140 144 146 180 182 186 212 216 296 312 326	1026455766996