Prime p₀= 2356489790729063567 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 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: Orange Kid
db: batch=81, k=10, 2 28 2 10 2

SPT(16)	2356488647820554033	0 26 30 44 50 66 96 114 146 164 194 210 216 230 234 260	-1142908509534
SPT(16)	2356488880859691691	0 12 42 58 60 70 78 88 120 130 138 148 150 166 196 208	-909869371876
TPT(14)	2356489271935437407	0 2 60 62 84 86 150 152 192 194 264 266 270 272	-518793626160
STPT(10)	2356489276208508767	0 2 42 44 72 74 102 104 144 146	-514520554800
SPT(16)	2356489595425459511	0 2 62 66 90 98 110 162 266 318 330 338 362 366 426 428	-195303604056
STPT(10)	2356489683177201599	0 2 18 20 30 32 42 44 60 62	-107551861968
STPT(10)	2356489961733604859	0 2 42 44 120 122 198 200 240 242	171004541292
STPT(10)	2356489999997902577	0 2 54 56 72 74 90 92 144 146	209268839010
SPT(16)	2356490024875819171	0 6 22 42 48 72 76 100 138 162 166 190 196 216 232 238	234146755604
SPT(16)	2356490034487276679	0 32 38 60 80 92 98 102 158 162 168 180 200 222 228 260	243758213112
TPT(14)	2356490058755197031	0 2 6 8 120 122 198 200 426 428 498 500 678 680	268026133464