Prime p₀= 2044738371999202697 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 6 74 16 8 18 90 24 34 24 90 18 8 16 74 6 (?)
a_n: 0 6 80 96 104 122 212 236 270 294 384 402 410 426 500 506
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: 506
Found by: Landjunge
db: batch=80, k=16, 6 74 16 8 18 90 24 34

SPT(16)	2044737600324922577	0 2 6 32 42 74 116 152 204 240 282 314 324 350 354 356	-771674280120
STPT(10)	2044737682995917051	0 2 6 8 18 20 30 32 36 38	-689003285646
STPT(10)	2044737821258258051	0 2 30 32 78 80 126 128 156 158	-550740944646
STPT(10)	2044737889881082211	0 2 6 8 48 50 90 92 96 98	-482118120486
TPT(14)	2044738087211647769	0 2 12 14 30 32 102 104 132 134 168 170 198 200	-284787554928
STPT(10)	2044738196020981337	0 2 30 32 60 62 90 92 120 122	-175978221360
SPT(16)	2044738671684070721	0 42 66 90 116 242 258 276 332 350 366 492 518 542 566 608	299684868024
SPT(16)	2044738677698612471	0 2 78 92 98 120 140 156 212 228 248 270 276 290 366 368	305699409774
SPT(16)	2044739045131249279	0 40 42 72 82 112 138 142 168 172 198 228 238 268 270 310	673132046582
SPT(16)	2044739098303260523	0 10 48 64 94 108 138 178 180 220 250 264 294 310 348 358	726304057826
SPT(16)	2044739102618261507	0 24 72 84 86 122 150 156 230 236 264 300 302 314 362 386	730619058810