Prime p₀= 2909367242025433961 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 46 2 28 2 40 2 28 2 16 2 (?)
a_n: 0 2 78 80 126 128 156 158 198 200 228 230 246 248
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: 248
Found by: Landjunge
db: batch=82, k=14, 76 46 28 40 28 16

SPT(16)	2909365965176693159	0 8 62 140 158 222 242 278 294 330 350 414 432 510 564 572	-1276848740802
TPT(14)	2909366081240124521	0 2 30 32 66 68 78 80 96 98 138 140 168 170	-1160785309440
SPT(16)	2909366471908389469	0 4 28 42 72 78 82 88 114 120 124 130 160 174 198 202	-770117044492
SPT(16)	2909366576028234389	0 30 44 92 110 200 204 222 242 260 264 354 372 420 434 464	-665997199572
SPT(16)	2909366670473298767	0 2 12 102 110 116 132 156 200 224 240 246 254 344 354 356	-571552135194
SPT(16)	2909366953992901799	0 42 78 108 132 180 194 222 260 288 302 350 374 404 440 482	-288032532162
STPT(10)	2909368257036731291	0 2 6 8 48 50 90 92 96 98	1015011297330
STPT(10)	2909368739522594519	0 2 18 20 30 32 42 44 60 62	1497497160558
STPT(10)	2909368863962438231	0 2 6 8 48 50 90 92 96 98	1621937004270
SPT(16)	2909369056275103999	0 22 48 58 84 142 148 180 352 384 390 448 474 484 510 532	1814249670038
STPT(10)	2909369529353676209	0 2 18 20 30 32 42 44 60 62	2287328242248