Prime p₀= 1092551003508723509 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 172 2 76 2 10 2 106 2 70 2 (?)
a_n: 0 2 78 80 252 254 330 332 342 344 450 452 522 524
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: 524
Found by: crashtech
db: batch=76, k=14, 76 172 76 10 106 70

SPT(16)	1092550701332574557	0 24 132 162 164 192 204 206 300 302 314 342 344 374 482 506	-302176148952
STPT(10)	1092550702696656479	0 2 12 14 90 92 168 170 180 182	-300812067030
TPT(14)	1092550749262954361	0 2 30 32 156 158 198 200 228 230 240 242 288 290	-254245769148
TPT(14)	1092550766964998189	0 2 120 122 132 134 168 170 270 272 342 344 378 380	-236543725320
SPT(16)	1092550785118578587	0 20 72 84 90 114 120 132 182 194 200 224 230 242 294 314	-218390144922
TPT(14)	1092550978060602197	0 2 54 56 102 104 210 212 252 254 282 284 294 296	-25448121312
STPT(10)	1092551079679367447	0 2 60 62 72 74 84 86 144 146	76170643938
STPT(10)	1092551421683673779	0 2 18 20 60 62 102 104 120 122	418174950270
STPT(10)	1092551455280641127	0 2 90 92 102 104 114 116 204 206	451771917618
STPT(10)	1092551538942174131	0 2 6 8 18 20 30 32 36 38	535433450622
SPT(16)	1092551913898942789	0 10 12 18 42 52 54 118 144 208 210 220 244 250 252 262	910390219280