Prime p₀= 2306561256661072511 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 10 2 28 2 28 2 76 2 58 2 (?)
a_n: 0 2 6 8 18 20 48 50 78 80 156 158 216 218
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: 218
Found by: FritzB
db: batch=81, k=14, 4 10 28 28 76 58

SPT(16)	2306560245128213287	0 16 70 132 174 192 204 250 276 322 334 352 394 456 510 526	-1011532859224
STPT(10)	2306560371432634529	0 2 42 44 60 62 78 80 120 122	-885228437982
SPT(16)	2306560535219032487	0 6 72 84 92 96 104 110 156 162 170 174 182 194 260 266	-721442040024
SPT(16)	2306560595610697549	0 58 70 78 90 100 118 160 162 204 222 232 244 252 264 322	-661050374962
SPT(16)	2306560788927206101	0 6 12 96 112 118 132 138 220 226 240 246 262 346 352 358	-467733866410
TPT(14)	2306560926139165301	0 2 90 92 156 158 216 218 240 242 258 260 348 350	-330521907210
SPT(16)	2306562415913308117	0 10 22 24 76 90 94 120 136 162 166 180 232 234 246 256	1159252235606
STPT(10)	2306562793642763057	0 2 84 86 132 134 180 182 264 266	1536981690546
SPT(16)	2306562835355885789	0 14 30 90 92 104 182 204 278 300 378 390 392 452 468 482	1578694813278
STPT(12)	2306562846680247851	0 2 36 38 48 50 78 80 90 92 126 128	1590019175340
SPT(16)	2306562900442086973	0 40 136 186 196 298 376 406 420 450 528 630 640 690 786 826	1643781014462