Prime p₀= 2568581645235650687 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: JayPi
db: batch=82, k=10, 2 22 2 16 2

SPT(16)	2568578652436335757	0 30 60 102 130 154 162 184 210 232 240 264 292 334 364 394	-2992799314930
STPT(10)	2568579209034948881	0 2 36 38 78 80 120 122 156 158	-2436200701806
STPT(12)	2568579331198386761	0 2 36 38 48 50 78 80 90 92 126 128	-2314037263926
TPT(14)	2568579967745756117	0 2 30 32 180 182 192 194 270 272 294 296 360 362	-1677489894570
TPT(14)	2568580337885298257	0 2 24 26 264 266 294 296 300 302 330 332 360 362	-1307350352430
SPT(16)	2568581010075766291	0 36 58 78 90 118 130 160 168 198 210 238 250 270 292 328	-635159884396
SPT(16)	2568581745379875443	0 56 60 140 168 194 206 210 344 348 360 386 414 494 498 554	100144224756
STPT(10)	2568582173648063759	0 2 18 20 30 32 42 44 60 62	528412413072
STPT(10)	2568582835656758909	0 2 18 20 30 32 42 44 60 62	1190421108222
SPT(16)	2568583058054796449	0 8 14 42 60 84 132 242 270 380 428 452 470 498 504 512	1412819145762
SPT(16)	2568583178551017479	0 8 24 48 74 92 108 120 122 134 150 168 194 218 234 242	1533315366792