Prime p₀= 3216238444538239187 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 10 2 10 2 58 2 64 2 10 2 (?)
a_n: 0 2 60 62 72 74 84 86 144 146 210 212 222 224
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: 224
Found by: vaughan
db: batch=83, k=14, 58 10 10 58 64 10

SPT(16)	3216237247983441289	0 4 12 60 88 114 130 150 202 222 238 264 292 340 348 352	-1196554797898
STPT(10)	3216237282809760161	0 2 78 80 138 140 198 200 276 278	-1161728479026
STPT(10)	3216237367997709827	0 2 30 32 72 74 114 116 144 146	-1076540529360
SPT(16)	3216237525122576057	0 24 36 96 146 230 252 266 270 284 306 390 440 500 512 536	-919415663130
SPT(16)	3216238002196189423	0 6 10 24 48 84 88 96 208 216 220 256 280 294 298 304	-442342049764
SPT(16)	3216238375071227581	0 6 12 22 40 60 70 82 126 138 148 168 186 196 202 208	-69467011606
STPT(10)	3216238444538239187	0 2 60 62 72 74 84 86 144 146	0
SPT(16)	3216238530047372761	0 18 22 46 52 78 88 126 172 210 220 246 252 276 280 298	85509133574
SPT(16)	3216238883124176201	0 12 62 92 102 140 216 222 350 356 432 470 480 510 560 572	438585937014
SPT(16)	3216239078606112947	0 6 12 120 146 212 216 254 342 380 384 450 476 584 590 596	634067873760
TPT(14)	3216239360935452737	0 2 72 74 84 86 132 134 144 146 174 176 210 212	916397213550