Prime p₀= 1006303024691310131 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 16 2 10 2 94 2 10 2 (?)
a_n: 0 2 30 32 60 62 78 80 90 92 186 188 198 200
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: 200
Found by: HenkM
db: batch=76, k=14, 28 28 16 10 94 10

TPT(14)	1006301948278185497	0 2 30 32 162 164 204 206 234 236 240 242 252 254	-1076413124634
SPT(16)	1006302003398928791	0 20 36 48 86 90 128 168 218 258 296 300 338 350 366 386	-1021292381340
SPT(16)	1006302149761809833	0 18 36 38 48 116 140 168 206 234 258 326 336 338 356 374	-874929500298
SPT(20)	1006302401721732629	0 2 42 54 68 98 128 134 182 230 282 330 378 384 414 444 458 470 510 512	-622969577502
STPT(10)	1006302471414896471	0 2 6 8 48 50 90 92 96 98	-553276413660
STPT(10)	1006302757463757581	0 2 36 38 78 80 120 122 156 158	-267227552550
SPT(16)	1006303044624052163	0 20 48 60 126 128 156 170 186 200 228 230 296 308 336 356	19932742032
SPT(13)	1006303281575667809	0 18 30 42 108 180 210 240 312 378 390 402 420	256884357678
SPT(16)	1006303493067633689	0 14 54 68 78 84 144 162 200 218 278 284 294 308 348 362	468376323558
STPT(10)	1006303688054347607	0 2 42 44 222 224 402 404 444 446	663363037476
SPT(16)	1006304139921586183	0 58 96 108 138 168 178 250 396 468 478 508 538 550 588 646	1115230276052