Prime p₀= 2865149841503132471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 100 2 16 2 40 2 10 2 34 2 (?)
a_n: 0 2 36 38 138 140 156 158 198 200 210 212 246 248
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: [SG]ATA-Rolf
db: batch=82, k=14, 34 100 16 40 10 34

SPT(16)	2865148577758031689	0 42 70 102 148 192 208 280 330 402 418 462 508 540 568 610	-1263745100782
STPT(10)	2865149018541003191	0 2 6 8 48 50 90 92 96 98	-822962129280
STPT(10)	2865149053423951109	0 2 48 50 90 92 132 134 180 182	-788079181362
STPT(10)	2865149589499895207	0 2 42 44 72 74 102 104 144 146	-252003237264
SPT(16)	2865149636556111011	0 6 8 42 66 78 90 120 128 158 170 182 206 240 242 248	-204947021460
STPT(10)	2865149835010689839	0 2 18 20 30 32 42 44 60 62	-6492442632
SPT(16)	2865150068664330947	0 42 56 92 114 180 192 194 222 224 236 302 324 360 374 416	227161198476
STPT(10)	2865150472182054179	0 2 12 14 30 32 48 50 60 62	630678921708
SPT(16)	2865150499251178709	0 44 48 72 74 104 120 132 140 152 168 198 200 224 228 272	657748046238
SPT(16)	2865150797805742673	0 8 30 80 108 128 134 156 188 210 216 236 264 314 336 344	956302610202
SPT(18)	2865150849844749127	0 16 60 112 126 132 142 184 210 256 282 324 334 340 354 406 450 466	1008341616656