Prime p₀= 120623893728938737 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 36 4 14 6 4 6 26 6 4 6 14 4 36 (?)
a_n: 0 36 40 54 60 64 70 96 102 106 112 126 130 166
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: 166
Found by: [SG-2W]Kurzer
db: batch=67, k=14, 36 4 14 6 4 6 26

SPT(14)	120623816575762811	0 42 56 80 110 188 192 236 240 318 348 372 386 428	-77153175926
TPT(12)	120623831385749369	0 2 12 14 60 62 138 140 168 170 252 254	-62343189368
SPT(14)	120623833652154671	0 56 60 86 108 138 152 156 170 200 222 248 252 308	-60076784066
SPT(14)	120623858666819143	0 4 48 88 94 100 108 160 168 174 180 220 264 268	-35062119594
SPT(14)	120623864159954977	0 22 42 96 156 174 180 226 232 250 310 364 384 406	-29568983760
SPT(14)	120623888310311843	0 6 20 44 56 74 78 86 90 108 120 144 158 164	-5418626894
SPT(14)	120623928774924719	0 2 72 102 134 140 152 162 174 180 212 242 312 314	35045985982
SPT(14)	120623950763963011	0 22 58 78 100 102 112 138 148 150 172 192 228 250	57035024274
SPT(16)	120623951145336307	0 76 84 100 102 120 126 154 162 190 196 214 216 232 240 316	57416397570
SPT(14)	120623964828768881	0 8 30 126 128 132 156 242 266 270 272 368 390 398	71099830144
SPT(14)	120623973626041343	0 38 44 84 128 150 188 216 254 276 320 360 366 404	79897102606