Prime p₀= 2782814907518055497 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 148 2 22 2 16 2 10 2 346 2 40 2 (?)
a_n: 0 2 150 152 174 176 192 194 204 206 552 554 594 596
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: 596
Found by: [SG-FC] hl
db: batch=82, k=14, 148 22 16 10 346 40

SPT(16)	2782813168732441721	0 48 56 60 86 116 120 122 126 128 132 162 188 192 200 248	-1738785613776
STPT(10)	2782813861689562157	0 2 30 32 72 74 114 116 144 146	-1045828493340
SPT(16)	2782813883190592817	0 2 12 14 20 54 104 144 152 192 242 276 282 284 294 296	-1024327462680
STPT(10)	2782814071886738801	0 2 6 8 18 20 30 32 36 38	-835631316696
SPT(16)	2782814082118375561	0 36 58 60 72 88 112 126 142 156 180 196 208 210 232 268	-825399679936
SPT(16)	2782814427919586251	0 6 10 28 72 78 112 126 142 156 190 196 240 258 262 268	-479598469246
SPT(16)	2782815159916365839	0 42 48 80 152 158 174 210 212 248 264 270 342 374 380 422	252398310342
STPT(10)	2782815983884677581	0 2 36 38 78 80 120 122 156 158	1076366622084
SPT(16)	2782816452313432891	0 10 28 30 42 82 156 186 262 292 366 406 418 420 438 448	1544795377394
STPT(10)	2782816603977712019	0 2 12 14 90 92 168 170 180 182	1696459656522
STPT(10)	2782816873795928831	0 2 36 38 78 80 120 122 156 158	1966277873334