Prime p₀= 1518424652309938559 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 10 2 28 2 88 2 34 2 (?)
a_n: 0 2 30 32 90 92 102 104 132 134 222 224 258 260
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: 260
Found by: TheKillerChicken
db: batch=78, k=14, 28 58 10 28 88 34

SPT(16)	1518423026303914879	0 12 30 40 78 88 108 120 130 142 162 172 210 220 238 250	-1626006023680
STPT(10)	1518423509978270801	0 2 6 8 48 50 90 92 96 98	-1142331667758
SPT(16)	1518423779898681041	0 50 60 68 86 96 116 138 140 162 182 192 210 218 228 278	-872411257518
SPT(16)	1518424139573313853	0 24 30 34 58 84 118 124 144 150 184 210 234 238 244 268	-512736624706
STPT(12)	1518424369719594497	0 2 12 14 24 26 30 32 42 44 54 56	-282590344062
STPT(10)	1518424424910906839	0 2 18 20 30 32 42 44 60 62	-227399031720
STPT(10)	1518425064414713051	0 2 36 38 78 80 120 122 156 158	412104774492
TPT(14)	1518425153995500869	0 2 42 44 60 62 138 140 198 200 222 224 228 230	501685562310
SPT(16)	1518425399397497009	0 14 38 42 44 60 74 80 132 138 152 168 170 174 198 212	747087558450
SPT(16)	1518425487439869227	0 24 50 84 116 126 146 174 326 354 374 384 416 450 476 500	835129930668
SPT(16)	1518425522703157567	0 4 10 22 64 70 94 144 262 312 336 342 384 396 402 406	870393219008