Prime p₀= 3015933438056980211 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 88 2 28 2 10 2 124 2 40 2 (?)
a_n: 0 2 78 80 168 170 198 200 210 212 336 338 378 380
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: 380
Found by: ginga
db: batch=82, k=14, 76 88 28 10 124 40

SPT(16)	3015932029446887261	0 32 50 62 90 96 120 132 266 278 302 308 336 348 366 398	-1408610092950
STPT(10)	3015932234504487869	0 2 18 20 30 32 42 44 60 62	-1203552492342
SPT(16)	3015932757640766321	0 66 68 78 96 102 140 152 276 288 326 332 350 360 362 428	-680416213890
SPT(16)	3015933206340486953	0 50 78 126 140 176 180 198 218 236 240 276 290 338 366 416	-231716493258
STPT(10)	3015933256835551601	0 2 6 8 48 50 90 92 96 98	-181221428610
SPT(18)	3015933317381449457	0 12 32 54 116 150 152 180 222 284 326 354 356 390 452 474 494 506	-120675530754
SPT(16)	3015933939107660777	0 6 12 20 24 42 72 84 92 104 134 152 156 164 170 176	501050680566
SPT(16)	3015934012669395361	0 10 108 118 162 196 208 222 316 330 342 376 420 430 528 538	574612415150
SPT(16)	3015934236417237479	0 14 18 32 42 50 54 110 192 248 252 260 270 284 288 302	798360257268
SPT(16)	3015934502027453731	0 22 60 102 112 142 156 196 216 256 270 300 310 352 390 412	1063970473520
SPT(16)	3015934583387195909	0 14 18 48 50 74 80 150 158 228 234 258 260 290 294 308	1145330215698