Prime p₀= 4092751798163893517 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 88 2 40 2 34 2 28 2 (?)
a_n: 0 2 30 32 42 44 132 134 174 176 210 212 240 242
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: 242
Found by: [AF>WildWildWest]Sebastien
db: batch=84, k=14, 28 10 88 40 34 28

SPT(13)	4092750542742079601	0 36 126 138 168 258 318 378 468 498 510 600 636	-1255421813916
STPT(10)	4092750545774243159	0 2 78 80 120 122 162 164 240 242	-1252389650358
TPT(14)	4092750856663662371	0 2 36 38 66 68 138 140 168 170 180 182 246 248	-941500231146
SPT(16)	4092750896798795663	0 38 60 68 80 90 104 126 158 180 194 204 216 224 246 284	-901365097854
SPT(16)	4092750941933669789	0 2 44 54 68 98 200 222 230 252 354 384 398 408 450 452	-856230223728
STPT(10)	4092751221741380249	0 2 18 20 60 62 102 104 120 122	-576422513268
SPT(16)	4092751969898375689	0 10 12 22 24 90 100 112 120 132 142 208 210 220 222 232	171734482172
SPT(16)	4092752063216492251	0 30 52 58 108 130 136 142 246 252 258 280 330 336 358 388	265052598734
STPT(10)	4092752157919079297	0 2 24 26 42 44 60 62 84 86	359755185780
SPT(16)	4092752228569520081	0 20 38 42 60 98 156 228 320 392 450 488 506 510 528 548	430405626564
TPT(14)	4092752363579194451	0 2 66 68 90 92 108 110 180 182 210 212 246 248	565415300934