Prime p₀= 2561771076102813719 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 136 2 76 2 40 2 10 2 (?)
a_n: 0 2 18 20 42 44 180 182 258 260 300 302 312 314
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: 314
Found by: JayPi
db: batch=82, k=14, 16 22 136 76 40 10

SPT(16)	2561770043395367657	0 2 6 24 56 62 74 132 164 222 234 240 272 290 294 296	-1032707446062
SPT(13)	2561770415512469267	0 30 84 120 156 210 240 270 324 360 396 450 480	-660590344452
SPT(16)	2561770663640789347	0 22 40 64 82 106 112 132 154 174 180 204 222 246 264 286	-412462024372
SPT(16)	2561770707476192077	0 10 40 54 94 144 150 154 162 166 172 222 262 276 306 316	-368626621642
SPT(16)	2561770973599267769	0 8 14 50 78 84 122 204 218 300 338 344 372 408 414 422	-102503545950
SPT(13)	2561771042764344211	0 36 66 78 108 126 138 150 168 198 210 240 276	-33338469508
SPT(16)	2561771684709580009	0 118 130 148 150 154 172 198 274 300 318 322 324 342 354 472	608606766290
STPT(10)	2561771913410485619	0 2 18 20 30 32 42 44 60 62	837307671900
STPT(10)	2561771966969685257	0 2 12 14 72 74 132 134 144 146	890866871538
STPT(10)	2561772012732546077	0 2 60 62 102 104 144 146 204 206	936629732358
SPT(16)	2561772096400270057	0 12 22 30 40 52 82 132 142 192 222 234 244 252 262 274	1020297456338