Prime p₀= 1235465601392686967 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 4 2 40 2 28 2 208 2 40 2 (?)
a_n: 0 2 84 86 90 92 132 134 162 164 372 374 414 416
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: 416
Found by: xii5ku
db: batch=77, k=14, 82 4 40 28 208 40

SPT(16)	1235464431408512623	0 10 16 24 54 84 106 118 156 168 190 220 250 258 264 274	-1169984174344
STPT(10)	1235464796144747261	0 2 36 38 78 80 120 122 156 158	-805247939706
TPT(16)	1235465017066563161	0 2 30 32 90 92 138 140 168 170 258 260 300 302 306 308	-584326123806
STPT(10)	1235465072274706709	0 2 42 44 60 62 78 80 120 122	-529117980258
SPT(18)	1235465234504228719	0 4 18 28 34 40 54 78 82 90 94 118 132 138 144 154 168 172	-366888458248
SPT(16)	1235465390841350783	0 14 44 56 90 98 104 170 174 240 246 254 288 300 330 344	-210551336184
STPT(10)	1235465843316505919	0 2 18 20 30 32 42 44 60 62	241923818952
SPT(16)	1235466487075075799	0 14 20 42 48 62 92 102 140 150 180 194 200 222 228 242	885682388832
STPT(10)	1235466627557150897	0 2 30 32 42 44 54 56 84 86	1026164463930
STPT(10)	1235466699376399727	0 2 30 32 42 44 54 56 84 86	1097983712760
STPT(10)	1235467318634832461	0 2 6 8 48 50 90 92 96 98	1717242145494