Prime p₀= 1069374499668987761 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 64 2 40 2 28 2 28 2 40 2 (?)
a_n: 0 2 30 32 96 98 138 140 168 170 198 200 240 242
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: 242
Found by: stoneageman
db: batch=76, k=14, 28 64 40 28 28 40

SPT(16)	1069373638222379401	0 10 18 30 46 52 66 88 90 112 126 132 148 160 168 178	-861446608360
SPT(16)	1069373713215024379	0 18 30 70 82 112 222 268 294 340 450 480 492 532 544 562	-786453963382
SPT(16)	1069374159059866249	0 22 28 52 84 142 148 178 204 234 240 298 330 354 360 382	-340609121512
SPT(16)	1069374236469617321	0 18 26 42 48 66 68 78 80 90 92 110 116 132 140 158	-263199370440
SPT(16)	1069374352463194483	0 28 46 60 76 118 160 166 180 186 228 270 286 300 318 346	-147205793278
STPT(10)	1069374495692470967	0 2 24 26 42 44 60 62 84 86	-3976516794
STPT(10)	1069374499668987857	0 2 42 44 72 74 102 104 144 146	96
SPT(16)	1069374639874216567	0 12 24 100 112 126 166 250 306 390 430 444 456 532 544 556	140205228806
SPT(16)	1069374861660314147	0 2 12 14 32 50 74 102 134 162 186 204 222 224 234 236	361991326386
STPT(10)	1069374985801798691	0 2 36 38 78 80 120 122 156 158	486132810930
STPT(10)	1069375006641131159	0 2 12 14 30 32 48 50 60 62	506972143398