Prime p₀= 1246936029667933877 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=77, k=10, 2 22 2 16 2

SPT(16)	1246935199630113859	0 48 94 130 150 258 264 270 328 334 340 448 468 504 550 598	-830037820018
STPT(12)	1246935343139887811	0 2 48 50 90 92 126 128 168 170 216 218	-686528046066
STPT(10)	1246935566150394047	0 2 42 44 72 74 102 104 144 146	-463517539830
SPT(16)	1246935570288951233	0 36 56 60 74 80 104 108 116 120 144 150 164 168 188 224	-459378982644
STPT(10)	1246935596544369671	0 2 30 32 60 62 90 92 120 122	-433123564206
STPT(10)	1246935724005498509	0 2 12 14 90 92 168 170 180 182	-305662435368
SPT(16)	1246936080866577667	0 40 52 60 82 150 154 166 180 192 196 264 286 294 306 346	51198643790
SPT(16)	1246936157917368547	0 52 54 94 132 144 154 186 250 282 292 304 342 382 384 436	128249434670
SPT(18)	1246936300754931607	0 30 34 46 142 144 280 294 304 402 412 426 562 564 660 672 676 706	271086997730
STPT(10)	1246936336436996501	0 2 6 8 18 20 30 32 36 38	306769062624
SPT(16)	1246936653347769641	0 50 90 96 116 126 236 242 330 336 446 456 476 482 522 572	623679835764