Prime p₀= 1251909865367952409 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 24 58 78 18 2 64 56 22 56 64 2 18 78 58 24 (?)
a_n: 0 24 82 160 178 180 244 300 322 378 442 444 462 540 598 622
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 622
Found by: Cruncher Pete
db: batch=77, k=16, 24 58 78 18 2 64 56 22

SPT(16)	1251909581718456289	0 18 24 30 54 90 114 132 150 168 192 228 252 258 264 282	-283649496120
STPT(10)	1251909600914818007	0 2 30 32 42 44 54 56 84 86	-264453134402
TPT(14)	1251909655098041627	0 2 72 74 162 164 240 242 294 296 312 314 330 332	-210269910782
STPT(10)	1251909679398452741	0 2 6 8 18 20 30 32 36 38	-185969499668
SPT(16)	1251909695136726091	0 12 22 70 72 88 100 120 148 168 180 196 198 246 256 268	-170231226318
STPT(12)	1251909696148959431	0 2 36 38 78 80 138 140 180 182 216 218	-169218992978
STPT(10)	1251909979646052437	0 2 60 62 72 74 84 86 144 146	114278100028
STPT(10)	1251910449267446831	0 2 36 38 78 80 120 122 156 158	583899494422
STPT(10)	1251910870203062891	0 2 6 8 48 50 90 92 96 98	1004835110482
SPT(16)	1251911051419923061	0 16 40 48 58 72 90 96 112 118 136 150 160 168 192 208	1186051970652
STPT(12)	1251911590194558581	0 2 30 32 78 80 198 200 246 248 276 278	1724826606172