Prime p₀= 2783751416775489239 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 82 2 88 2 4 2 52 2 28 2 (?)
a_n: 0 2 78 80 162 164 252 254 258 260 312 314 342 344
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: 344
Found by: [SG-FC] hl
db: batch=82, k=14, 76 82 88 4 52 28

SPT(16)	2783749951344045137	0 6 26 42 56 62 90 114 122 146 174 180 194 210 230 236	-1465431444102
SPT(16)	2783750429354038943	0 38 60 120 128 138 168 170 234 236 266 276 284 344 366 404	-987421450296
SPT(16)	2783750563519916609	0 14 48 54 80 92 134 138 164 168 210 222 248 254 288 302	-853255572630
STPT(10)	2783750873182232711	0 2 6 8 18 20 30 32 36 38	-543593256528
SPT(16)	2783750963845085551	0 16 28 78 88 100 102 172 186 256 258 270 280 330 342 358	-452930403688
TPT(14)	2783751086782251029	0 2 12 14 42 44 78 80 120 122 162 164 168 170	-329993238210
SPT(16)	2783751494677862777	0 50 96 102 120 126 132 146 180 194 200 206 224 230 276 326	77902373538
SPT(16)	2783752583141008741	0 6 28 30 48 70 108 118 150 160 198 220 238 240 262 268	1166365519502
STPT(10)	2783753455454437589	0 2 48 50 90 92 132 134 180 182	2038678948350
SPT(16)	2783753546264724547	0 24 42 64 106 132 156 204 232 280 304 330 372 394 412 436	2129489235308
STPT(10)	2783753563017515951	0 2 36 38 78 80 120 122 156 158	2146242026712