Prime p₀= 2571976221012101711 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 274 2 22 2 4 2 82 2 28 2 4 2 (?)
a_n: 0 2 276 278 300 302 306 308 390 392 420 422 426 428
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: 428
Found by: RFGuy_KCCO
db: batch=82, k=14, 274 22 4 82 28 4

SPT(16)	2571974712831134977	0 4 16 22 46 100 112 120 136 144 156 210 234 240 252 256	-1508180966734
STPT(10)	2571975352144079207	0 2 42 44 72 74 102 104 144 146	-868868022504
SPT(16)	2571975730242451571	0 38 56 80 86 90 98 120 176 198 206 210 216 240 258 296	-490769650140
SPT(16)	2571975730325318693	0 36 48 68 78 98 126 150 164 188 216 236 246 266 278 314	-490686783018
STPT(10)	2571976112064684749	0 2 48 50 90 92 132 134 180 182	-108947416962
SPT(16)	2571976195813610603	0 20 68 176 188 240 248 266 288 306 314 366 378 486 534 554	-25198491108
SPT(16)	2571976726910950553	0 36 50 56 78 80 138 150 164 176 234 236 258 264 278 314	505898848842
TPT(14)	2571976731516721187	0 2 42 44 114 116 162 164 180 182 192 194 204 206	510504619476
SPT(16)	2571978108179369639	0 12 38 74 80 84 122 138 254 270 308 312 318 354 380 392	1887167267928
SPT(16)	2571978254860679389	0 30 48 58 60 84 112 204 238 330 358 382 384 394 412 442	2033848577678
SPT(16)	2571978426473266549	0 40 84 88 144 204 228 382 390 544 568 628 684 688 732 772	2205461164838