Prime p₀= 1044723956641625147 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 84 86
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: 86
Found by: gemini8
db: batch=76, k=10, 2 22 2 16 2

SPT(16)	1044723112748449681	0 10 18 22 40 46 136 172 186 222 312 318 336 340 348 358	-843893175466
STPT(10)	1044723170468690927	0 2 30 32 42 44 54 56 84 86	-786172934220
SPT(13)	1044723203621317111	0 42 78 90 132 138 150 162 168 210 222 258 300	-753020308036
STPT(10)	1044723411913330307	0 2 54 56 72 74 90 92 144 146	-544728294840
STPT(10)	1044723443241918491	0 2 6 8 18 20 30 32 36 38	-513399706656
STPT(10)	1044723449351735759	0 2 48 50 90 92 132 134 180 182	-507289889388
STPT(10)	1044724160335368341	0 2 6 8 48 50 90 92 96 98	203693743194
STPT(10)	1044724206839541341	0 2 36 38 78 80 120 122 156 158	250197916194
SPT(16)	1044724214402103541	0 40 60 88 166 208 250 256 300 306 348 390 468 496 516 556	257760478394
SPT(16)	1044724381567333463	0 6 24 38 44 78 84 104 150 170 176 210 216 230 248 254	424925708316
SPT(16)	1044724405038450931	0 6 46 48 58 106 112 130 198 216 222 270 280 282 322 328	448396825784