Prime p₀= 1156002747509486759 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 148 2 16 2 28 2 148 2 106 2 (?)
a_n: 0 2 42 44 192 194 210 212 240 242 390 392 498 500
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: 500
Found by: Megacruncher
db: batch=77, k=14, 40 148 16 28 148 106

SPT(16)	1156001806480171943	0 24 36 48 80 96 108 146 168 206 218 234 266 278 290 314	-941029314816
SPT(16)	1156001858494814803	0 6 16 30 66 120 136 154 156 174 190 244 280 294 304 310	-889014671956
SPT(16)	1156002288128815319	0 14 24 44 80 84 110 132 212 234 260 264 300 320 330 344	-459380671440
SPT(16)	1156002309058914301	0 6 28 88 90 112 130 132 166 168 186 208 210 270 292 298	-438450572458
SPT(16)	1156002535250585521	0 10 28 48 76 78 90 186 202 298 310 312 340 360 378 388	-212258901238
TPT(14)	1156002719810097371	0 2 60 62 78 80 198 200 216 218 456 458 546 548	-27699389388
STPT(10)	1156002844747473599	0 2 30 32 60 62 90 92 120 122	97237986840
STPT(10)	1156002855925382747	0 2 42 44 72 74 102 104 144 146	108415895988
SPT(16)	1156003060846221871	0 28 112 142 156 232 252 280 288 316 336 412 426 456 540 568	313336735112
SPT(16)	1156003527289092887	0 14 66 86 126 140 146 164 192 210 216 230 270 290 342 356	779779606128
SPT(16)	1156003899142289969	0 2 18 30 32 98 104 144 188 228 234 300 302 314 330 332	1151632803210