Prime p₀= 1016251505499520061 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 34 2 40 2 40 2 34 2 (?)
a_n: 0 2 36 38 78 80 120 122 156 158
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: 158
Found by: Theadalus
db: batch=76, k=10, 2 34 2 40 2

SPT(16)	1016250702433772731	0 30 48 106 126 132 190 238 360 408 466 472 492 550 568 598	-803065747330
STPT(10)	1016250846586012559	0 2 18 20 30 32 42 44 60 62	-658913507502
SPT(16)	1016250999216620359	0 30 52 70 78 82 100 114 148 162 180 184 192 210 232 262	-506282899702
STPT(10)	1016251131906461807	0 2 30 32 72 74 114 116 144 146	-373593058254
SPT(16)	1016251209417469127	0 42 56 110 116 126 222 242 324 344 440 450 456 510 524 566	-296082050934
SPT(16)	1016251297250889473	0 14 20 30 36 104 120 126 224 230 246 314 320 330 336 350	-208248630588
STPT(10)	1016251645442230397	0 2 30 32 72 74 114 116 144 146	139942710336
STPT(10)	1016251780093049411	0 2 6 8 18 20 30 32 36 38	274593529350
STPT(10)	1016251932658806617	0 2 54 56 72 74 90 92 144 146	427159286556
SPT(16)	1016252766969725941	0 6 18 28 42 108 112 118 120 126 130 196 210 220 232 238	1261470205880
SPT(16)	1016252818710580177	0 4 24 30 46 60 130 132 154 156 226 240 256 262 282 286	1313211060116