Prime p₀= 2311264689302728889 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 46 2 10 2 34 2 40 2 (?)
a_n: 0 2 30 32 72 74 120 122 132 134 168 170 210 212
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: 212
Found by: MarkRBright
db: batch=81, k=14, 28 40 46 10 34 40

SPT(16)	2311262455748379403	0 36 40 76 96 124 168 184 270 286 330 358 378 414 418 454	-2233554349486
SPT(16)	2311262590324848317	0 44 54 72 132 170 174 182 204 212 216 254 314 332 342 386	-2098977880572
SPT(16)	2311262996386667357	0 12 62 86 104 110 116 132 194 210 216 222 240 264 314 326	-1692916061532
STPT(10)	2311263212545676531	0 2 6 8 18 20 30 32 36 38	-1476757052358
SPT(16)	2311263305827313869	0 28 30 54 82 100 108 120 142 154 162 180 208 232 234 262	-1383475415020
SPT(16)	2311263487522003439	0 90 120 132 140 150 182 188 204 210 242 252 260 272 302 392	-1201780725450
STPT(10)	2311264925177706761	0 2 6 8 48 50 90 92 96 98	235874977872
SPT(16)	2311264981513070789	0 8 12 62 84 108 114 150 152 188 194 218 240 290 294 302	292210341900
STPT(10)	2311265051025105347	0 2 42 44 72 74 102 104 144 146	361722376458
SPT(16)	2311265262201972049	0 4 30 88 114 178 198 208 240 250 270 334 360 418 444 448	572899243160
SPT(16)	2311265436476651989	0 22 48 70 90 120 138 162 178 202 220 250 270 292 318 340	747173923100