Prime p₀= 2991728152790144561 starts a Symmetric tuple of 20 consecutive primes (SPT).
d_n: 0 6 50 10 62 12 36 40 44 18 40 18 44 40 36 12 62 10 50 6 (?)
a_n: 0 6 56 66 128 140 176 216 260 278 318 336 380 420 456 468 530 540 590 596
All 20 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 596
Found by: Roadranner
db: batch=82, k=20, 6 50 10 62 12 36 40 44 18 40

STPT(10)	2991727405841363219	0 2 18 20 30 32 42 44 60 62	-746948781342
SPT(16)	2991727634280497257	0 10 36 40 70 82 94 96 190 192 204 216 246 250 276 286	-518509647304
SPT(13)	2991727925609004697	0 114 120 162 174 180 252 324 330 342 384 390 504	-227181139864
STPT(10)	2991728005195232591	0 2 36 38 78 80 120 122 156 158	-147594911970
SPT(16)	2991728102947564597	0 4 12 16 24 60 82 96 100 114 136 172 180 184 192 196	-49842579964
STPT(10)	2991728114472591677	0 2 30 32 42 44 54 56 84 86	-38317552884
SPT(16)	2991728217407519921	0 2 126 168 182 200 206 242 366 402 408 426 440 482 606 608	64617375360
SPT(16)	2991728232881044801	0 28 42 72 78 82 100 138 172 210 228 232 238 268 282 310	80090900240
SPT(16)	2991728529016087057	0 4 10 22 36 64 72 126 130 184 192 220 234 246 252 256	376225942496
SPT(16)	2991729256021492027	0 12 52 54 70 112 132 192 202 262 282 324 340 342 382 394	1103231347466
STPT(10)	2991729719603183717	0 2 54 56 72 74 90 92 144 146	1566813039156