Prime p₀= 1233809894935415639 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 52 2 118 2 28 2 4 2 130 2 (?)
a_n: 0 2 78 80 132 134 252 254 282 284 288 290 420 422
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: 422
Found by: Theadalus
db: batch=77, k=14, 76 52 118 28 4 130

SPT(16)	1233808710747113929	0 24 42 54 88 102 120 138 154 172 190 204 238 250 268 292	-1184188301710
STPT(10)	1233808824911335469	0 2 18 20 30 32 42 44 60 62	-1070024080170
SPT(16)	1233809024638537433	0 30 36 48 60 98 146 186 188 228 276 314 326 338 344 374	-870296878206
STPT(10)	1233809114915826809	0 2 42 44 90 92 138 140 180 182	-780019588830
SPT(16)	1233809324774656127	0 12 24 44 50 60 72 80 114 122 134 144 150 170 182 194	-570160759512
SPT(16)	1233809765702725777	0 40 52 90 96 142 150 166 186 202 210 256 262 300 312 352	-129232689862
STPT(10)	1233810106403150399	0 2 12 14 30 32 48 50 60 62	211467734760
SPT(16)	1233810198600936233	0 6 30 110 180 224 228 258 266 296 300 344 414 494 518 524	303665520594
SPT(16)	1233810201184914763	0 36 54 120 124 126 138 156 238 256 268 270 274 340 358 394	306249499124
SPT(16)	1233810282499218509	0 2 50 68 72 120 134 140 222 228 242 290 294 312 360 362	387563802870
SPT(16)	1233810328366866737	0 12 90 126 146 194 204 222 224 242 252 300 320 356 434 446	433431451098