Prime p₀= 1556691841935915197 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 100 2 76 2 100 2 28 2 40 2 (?)
a_n: 0 2 60 62 162 164 240 242 342 344 372 374 414 416
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=78, k=14, 58 100 76 100 28 40

SPT(16)	1556690383118983999	0 64 90 130 150 160 168 174 208 214 222 232 252 292 318 382	-1458816931198
STPT(10)	1556690995336993301	0 2 30 32 60 62 90 92 120 122	-846598921896
SPT(20)	1556691065834311709	0 18 42 44 54 60 68 84 92 102 110 120 128 144 152 158 168 170 194 212	-776101603488
SPT(16)	1556691180070722341	0 32 42 72 132 150 156 192 266 302 308 326 386 416 426 458	-661865192856
SPT(16)	1556691268265102867	0 2 6 32 66 120 156 162 170 176 212 266 300 326 330 332	-573670812330
STPT(10)	1556691641857802531	0 2 6 8 48 50 90 92 96 98	-200078112666
STPT(10)	1556691987209921867	0 2 30 32 42 44 54 56 84 86	145274006670
STPT(10)	1556692117008948077	0 2 54 56 72 74 90 92 144 146	275073032880
TPT(14)	1556692387146043559	0 2 18 20 42 44 102 104 150 152 168 170 240 242	545210128362
STPT(10)	1556692644695446847	0 2 30 32 42 44 54 56 84 86	802759531650
STPT(10)	1556692974427776137	0 2 30 32 42 44 54 56 84 86	1132491860940