Prime p₀= 1290459141880187729 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 40 2 76 2 70 2 16 2 (?)
a_n: 0 2 30 32 48 50 90 92 168 170 240 242 258 260
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: HenkM
db: batch=77, k=14, 28 16 40 76 70 16

STPT(10)	1290457804170774929	0 2 18 20 30 32 42 44 60 62	-1337709412800
SPT(16)	1290457971780004717	0 70 82 106 126 156 214 226 270 282 340 370 390 414 426 496	-1170100183012
SPT(16)	1290458271122186039	0 14 20 30 32 74 84 90 152 158 168 210 212 222 228 242	-870758001690
STPT(12)	1290458307779454677	0 2 12 14 42 44 90 92 120 122 132 134	-834100733052
SPT(16)	1290458369847302443	0 6 16 36 76 88 100 118 126 144 156 168 208 228 238 244	-772032885286
SPT(16)	1290459133243964161	0 18 78 102 106 126 168 186 202 220 262 282 286 310 370 388	-8636223568
SPT(16)	1290459352516199533	0 6 24 28 90 96 126 156 178 208 238 244 306 310 328 334	210636011804
STPT(10)	1290459437655885191	0 2 30 32 78 80 126 128 156 158	295775697462
SPT(16)	1290459903820074263	0 24 44 68 90 104 134 168 176 210 240 254 276 300 320 344	761939886534
STPT(10)	1290460187583276959	0 2 18 20 30 32 42 44 60 62	1045703089230
SPT(16)	1290460324294185071	0 30 48 60 102 108 132 150 258 276 300 306 348 360 378 408	1182413997342