Prime p₀= 2363257910584638827 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 88 2 106 2 28 2 10 2 16 2 (?)
a_n: 0 2 42 44 132 134 240 242 270 272 282 284 300 302
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: 302
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 40 88 106 28 10 16

SPT(18)	2363257640222744827	0 4 24 46 66 70 72 84 126 160 202 214 216 220 240 262 282 286	-270361894000
TPT(14)	2363257645027256279	0 2 78 80 168 170 222 224 282 284 360 362 432 434	-265557382548
SPT(16)	2363257655840546909	0 8 20 30 48 72 80 90 122 132 140 164 182 192 204 212	-254744091918
SPT(16)	2363257697671168889	0 12 38 104 114 128 132 140 162 170 174 188 198 264 290 302	-212913469938
STPT(10)	2363257700722422311	0 2 66 68 108 110 150 152 216 218	-209862216516
STPT(10)	2363257720108593167	0 2 30 32 72 74 114 116 144 146	-190476045660
STPT(10)	2363257924169427821	0 2 6 8 48 50 90 92 96 98	13584788994
SPT(16)	2363257930064023829	0 20 68 134 158 168 170 200 282 312 314 324 348 414 462 482	19479385002
SPT(16)	2363258432722786691	0 8 42 66 72 86 102 120 158 176 192 206 212 236 270 278	522138147864
SPT(16)	2363258462107938623	0 8 54 68 78 120 128 156 158 186 194 236 246 260 306 314	551523299796
TPT(14)	2363260247809078997	0 2 84 86 120 122 234 236 252 254 264 266 372 374	2337224440170