Prime p₀= 1588472025433782677 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: emoga
db: batch=78, k=10, 2 22 2 16 2

SPT(16)	1588470513062655823	0 66 100 154 156 168 174 198 256 280 286 298 300 354 388 454	-1512371126854
STPT(10)	1588470911587860239	0 2 18 20 60 62 102 104 120 122	-1113845922438
SPT(16)	1588470943592899097	0 6 26 30 44 54 56 62 84 90 92 102 116 120 140 146	-1081840883580
TPT(14)	1588471252100651909	0 2 12 14 18 20 48 50 72 74 102 104 132 134	-773333130768
STPT(10)	1588471541926201277	0 2 90 92 102 104 114 116 204 206	-483507581400
SPT(13)	1588471549088360333	0 48 60 66 96 108 138 168 180 210 216 228 276	-476345422344
SPT(16)	1588472877391479631	0 52 60 82 88 96 100 102 166 168 172 180 186 208 216 268	851957696954
SPT(16)	1588473120802699699	0 24 58 94 150 178 198 220 228 250 270 298 354 390 424 448	1095368917022
STPT(10)	1588473659793082157	0 2 30 32 42 44 54 56 84 86	1634359299480
STPT(10)	1588473675030688001	0 2 6 8 48 50 90 92 96 98	1649596905324
SPT(16)	1588474528357269653	0 20 50 60 66 156 168 188 228 248 260 350 356 366 396 416	2502923486976