Prime p₀= 2044737682995917051 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 38
Found by: Landjunge
db: batch=80, k=10, 2 4 2 10 2

SPT(16)	2044735316979569707	0 64 70 76 84 114 124 136 180 192 202 232 240 246 252 316	-2366016347344
STPT(10)	2044735495695536087	0 2 42 44 132 134 222 224 264 266	-2187300380964
SPT(16)	2044736105076142327	0 22 36 72 100 106 126 154 252 280 300 306 334 370 384 406	-1577919774724
SPT(16)	2044736595010860241	0 22 58 106 142 156 162 208 270 316 322 336 372 420 456 478	-1087985056810
STPT(10)	2044736897516950067	0 2 12 14 72 74 132 134 144 146	-785478966984
SPT(16)	2044737600324922577	0 2 6 32 42 74 116 152 204 240 282 314 324 350 354 356	-82670994474
STPT(10)	2044737821258258051	0 2 30 32 78 80 126 128 156 158	138262341000
STPT(10)	2044737889881082211	0 2 6 8 48 50 90 92 96 98	206885165160
TPT(14)	2044738087211647769	0 2 12 14 30 32 102 104 132 134 168 170 198 200	404215730718
STPT(10)	2044738196020981337	0 2 30 32 60 62 90 92 120 122	513025064286
SPT(16)	2044738371999202697	0 6 80 96 104 122 212 236 270 294 384 402 410 426 500 506	689003285646