Prime p₀= 1580042349514717721 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 70 2 28 2 64 2 58 2 40 2 (?)
a_n: 0 2 78 80 150 152 180 182 246 248 306 308 348 350
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: 350
Found by: Icecold
db: batch=78, k=14, 76 70 28 64 58 40

SPT(20)	1580041019277793861	0 6 22 48 96 118 132 136 210 220 288 298 372 376 390 412 460 486 502 508	-1330236923860
TPT(14)	1580041303450096187	0 2 24 26 72 74 114 116 120 122 150 152 162 164	-1046064621534
SPT(16)	1580041463761871603	0 36 54 108 110 114 180 246 308 374 440 444 446 500 518 554	-885752846118
STPT(10)	1580041935230982281	0 2 36 38 78 80 120 122 156 158	-414283735440
SPT(16)	1580042080346640709	0 18 28 54 64 94 102 112 120 130 138 168 178 204 214 232	-269168077012
SPT(16)	1580042175019603901	0 26 68 86 102 126 128 180 188 240 242 266 282 300 342 368	-174495113820
SPT(16)	1580042525146853543	0 26 68 90 128 138 156 188 306 338 356 366 404 426 468 494	175632135822
SPT(16)	1580042630165090389	0 18 28 60 78 162 232 250 270 288 358 442 460 492 502 520	280650372668
STPT(10)	1580042672151120299	0 2 48 50 90 92 132 134 180 182	322636402578
SPT(16)	1580043080835073819	0 24 34 70 84 90 108 118 174 184 202 208 222 258 268 292	731320356098
SPT(16)	1580043143813402029	0 4 34 60 84 90 100 102 112 114 124 130 154 180 210 214	794298684308