Prime p₀= 4044859993561212167 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: Alnitak2019
db: batch=84, k=10, 2 22 2 16 2

STPT(10)	4044858207806390657	0 2 12 14 72 74 132 134 144 146	-1785754821510
STPT(10)	4044858361260057161	0 2 6 8 18 20 30 32 36 38	-1632301155006
SPT(16)	4044858816433429103	0 68 90 104 140 158 174 186 218 230 246 264 300 314 336 404	-1177127783064
TPT(14)	4044859054976314787	0 2 42 44 60 62 102 104 120 122 132 134 210 212	-938584897380
TPT(14)	4044859633979922227	0 2 42 44 54 56 114 116 162 164 222 224 240 242	-359581289940
STPT(10)	4044859790842096979	0 2 18 20 30 32 42 44 60 62	-202719115188
STPT(10)	4044860233063067771	0 2 108 110 138 140 168 170 276 278	239501855604
SPT(16)	4044860473669718839	0 10 22 30 82 100 114 132 142 160 174 192 244 252 264 274	480108506672
STPT(10)	4044860578059329627	0 2 30 32 42 44 54 56 84 86	584498117460
STPT(10)	4044860784808041101	0 2 36 38 78 80 120 122 156 158	791246828934
STPT(10)	4044861140426931677	0 2 30 32 72 74 114 116 144 146	1146865719510