Prime p₀= 1123427497860692639 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 10 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 42 44 60 62
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: 62
Found by: JonS
db: batch=76, k=10, 2 16 2 10 2

SPT(16)	1123426474210108037	0 12 26 54 56 62 72 144 182 254 264 270 272 300 314 326	-1023650584602
STPT(12)	1123426664378051981	0 2 6 8 48 50 78 80 120 122 126 128	-833482640658
SPT(16)	1123426679760666287	0 2 14 62 74 86 96 110 186 200 210 222 234 282 294 296	-818100026352
SPT(16)	1123426748632867051	0 28 60 66 126 156 162 226 282 346 352 382 442 448 480 508	-749227825588
STPT(10)	1123426811112860039	0 2 42 44 60 62 78 80 120 122	-686747832600
STPT(10)	1123427045533657157	0 2 42 44 72 74 102 104 144 146	-452327035482
STPT(10)	1123427619608697617	0 2 30 32 42 44 54 56 84 86	121748004978
STPT(10)	1123427806547503157	0 2 30 32 42 44 54 56 84 86	308686810518
SPT(16)	1123428073743078109	0 24 30 52 70 112 114 132 160 178 180 222 240 262 268 292	575882385470
SPT(16)	1123428254681083829	0 60 90 92 102 122 144 164 168 188 210 230 240 242 272 332	756820391190
STPT(10)	1123429029864761687	0 2 60 62 72 74 84 86 144 146	1532004069048