Prime p₀= 1082023378622818277 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 52 2 136 2 70 2 28 2 16 2 (?)
a_n: 0 2 60 62 114 116 252 254 324 326 354 356 372 374
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: 374
Found by: stoneageman
db: batch=76, k=14, 58 52 136 70 28 16

SPT(16)	1082022375287767391	0 18 48 56 60 86 168 300 308 440 522 548 552 560 590 608	-1003335050886
STPT(10)	1082022627268992359	0 2 18 20 30 32 42 44 60 62	-751353825918
TPT(14)	1082022868570847891	0 2 48 50 78 80 186 188 198 200 216 218 270 272	-510051970386
SPT(16)	1082023137077135779	0 18 28 40 54 88 100 130 162 192 204 238 252 264 274 292	-241545682498
SPT(16)	1082023144100208341	0 30 78 150 182 206 212 218 240 246 252 276 308 380 428 458	-234522609936
STPT(10)	1082023225465379297	0 2 90 92 102 104 114 116 204 206	-153157438980
STPT(10)	1082023464864270527	0 2 30 32 42 44 54 56 84 86	86241452250
SPT(16)	1082024179843142467	0 12 52 64 72 94 106 162 214 270 282 304 312 324 364 376	801220324190
STPT(10)	1082024333308609679	0 2 18 20 30 32 42 44 60 62	954685791402
STPT(10)	1082024390025915767	0 2 30 32 72 74 114 116 144 146	1011403097490
STPT(10)	1082024436875560811	0 2 6 8 48 50 90 92 96 98	1058252742534