Prime p₀= 2959786688082461519 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 58 2 76 2 28 2 22 2 28 2 (?)
a_n: 0 2 60 62 120 122 198 200 228 230 252 254 282 284
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: 284
Found by: Orange Kid
db: batch=82, k=14, 58 58 76 28 22 28

STPT(10)	2959785793677148487	0 2 84 86 102 104 120 122 204 206	-894405313032
SPT(16)	2959785925821269599	0 10 22 48 52 60 64 82 90 108 112 120 124 150 162 172	-762261191920
TPT(14)	2959786082922430457	0 2 54 56 90 92 132 134 150 152 180 182 192 194	-605160031062
TPT(14)	2959786164243086051	0 2 18 20 126 128 150 152 156 158 198 200 306 308	-523839375468
STPT(10)	2959786267932857549	0 2 18 20 30 32 42 44 60 62	-420149603970
SPT(16)	2959786550560567061	0 12 20 42 48 66 68 78 80 90 92 110 116 138 146 158	-137521894458
SPT(16)	2959786962963266269	0 30 78 192 198 204 264 282 360 378 438 444 450 564 612 642	274880804750
STPT(10)	2959787073854427911	0 2 6 8 48 50 90 92 96 98	385771966392
STPT(12)	2959787914990060697	0 2 12 14 30 32 72 74 90 92 102 104	1226907599178
SPT(16)	2959788382903734281	0 42 48 98 120 126 152 180 308 336 362 368 390 440 446 488	1694821272762
TPT(14)	2959788642749205149	0 2 42 44 78 80 120 122 150 152 180 182 210 212	1954666743630