Prime p₀= 1079723982678342581 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 34 2 202 2 34 2 52 2 58 2 (?)
a_n: 0 2 30 32 66 68 270 272 306 308 360 362 420 422
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: 422
Found by: crashtech
db: batch=76, k=14, 28 34 202 34 52 58

STPT(10)	1079722914796581239	0 2 18 20 30 32 42 44 60 62	-1067881761342
SPT(20)	1079723246381283677	0 12 20 24 56 104 116 140 144 162 164 182 186 210 222 270 302 306 314 326	-736297058904
SPT(16)	1079723392046213143	0 40 48 76 106 124 126 144 190 208 210 228 258 286 294 334	-590632129438
STPT(10)	1079723426061984029	0 2 18 20 30 32 42 44 60 62	-556616358552
SPT(16)	1079723462101659629	0 24 30 48 72 114 132 140 192 200 218 260 284 302 308 332	-520576682952
STPT(10)	1079723732585096741	0 2 6 8 18 20 30 32 36 38	-250093245840
SPT(16)	1079724108824113717	0 4 12 34 60 70 82 96 250 264 276 286 312 334 342 346	126145771136
SPT(16)	1079724148762154419	0 28 52 54 72 82 84 108 184 208 210 220 238 240 264 292	166083811838
STPT(10)	1079724216146079377	0 2 30 32 42 44 54 56 84 86	233467736796
STPT(10)	1079724244403553167	0 2 42 44 72 74 102 104 144 146	261725210586
SPT(16)	1079724661941784081	0 6 12 46 90 112 130 132 136 138 156 178 222 256 262 268	679263441500