Prime p₀= 2679648029309486357 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 124 2 28 2 52 2 94 2 10 2 (?)
a_n: 0 2 24 26 150 152 180 182 234 236 330 332 342 344
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: 344
Found by: [SG-FC] hl
db: batch=82, k=14, 22 124 28 52 94 10

SPT(16)	2679645728701475939	0 38 54 60 62 80 98 104 108 114 132 150 152 158 174 212	-2300608010418
SPT(16)	2679646931540333387	0 20 24 42 150 210 224 230 234 240 254 314 422 440 444 464	-1097769152970
SPT(16)	2679647031831062593	0 46 70 84 88 100 108 114 130 136 144 156 160 174 198 244	-997478423764
STPT(10)	2679647170491180467	0 2 30 32 42 44 54 56 84 86	-858818305890
SPT(16)	2679647296779796813	0 10 16 18 30 40 66 78 88 100 126 136 148 150 156 166	-732529689544
SPT(16)	2679647828497379951	0 30 66 72 102 122 128 150 158 180 186 206 236 242 278 308	-200812106406
SPT(16)	2679648671503507721	0 8 12 20 30 36 98 108 110 120 182 188 198 206 210 218	642194021364
STPT(10)	2679648926998993091	0 2 6 8 18 20 30 32 36 38	897689506734
STPT(10)	2679649216632980507	0 2 24 26 42 44 60 62 84 86	1187323494150
STPT(10)	2679650162263756037	0 2 30 32 72 74 114 116 144 146	2132954269680
STPT(10)	2679650179513011707	0 2 30 32 60 62 90 92 120 122	2150203525350