Prime p₀= 2326714564339013501 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 28 2 250 2 88 2 16 2 (?)
a_n: 0 2 30 32 48 50 78 80 330 332 420 422 438 440
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: 440
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 28 16 28 250 88 16

SPT(16)	2326714046507194427	0 42 44 84 114 174 224 252 284 312 362 422 452 492 494 536	-517831819074
STPT(10)	2326714050661576781	0 2 6 8 18 20 30 32 36 38	-513677436720
STPT(10)	2326714218556924631	0 2 30 32 120 122 210 212 240 242	-345782088870
SPT(16)	2326714219966967927	0 12 26 42 54 74 84 110 126 152 162 182 194 210 224 236	-344372045574
STPT(10)	2326714279658358671	0 2 6 8 48 50 90 92 96 98	-284680654830
SPT(16)	2326714414499455009	0 28 42 78 102 124 138 144 148 154 168 190 214 250 264 292	-149839558492
TPT(14)	2326714903295870159	0 2 42 44 48 50 72 74 78 80 210 212 252 254	338956856658
SPT(16)	2326715068322413651	0 22 28 36 60 72 82 88 120 126 136 148 172 180 186 208	503983400150
TPT(14)	2326715618348583731	0 2 78 80 96 98 120 122 150 152 276 278 348 350	1054009570230
SPT(16)	2326715659462102897	0 24 30 76 84 114 120 126 184 190 196 226 234 280 286 310	1095123089396
SPT(16)	2326715755431862643	0 66 90 144 158 164 168 210 224 266 270 276 290 344 368 434	1191092849142