Prime p₀= 1268550734021943257 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 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: Megacruncher
db: batch=77, k=10, 2 10 2 28 2

STPT(10)	1268549307355340111	0 2 6 8 48 50 90 92 96 98	-1426666603146
TPT(14)	1268549420524753979	0 2 150 152 162 164 252 254 318 320 498 500 540 542	-1313497189278
SPT(16)	1268549549322750803	0 38 50 84 120 138 164 170 174 180 206 224 260 294 306 344	-1184699192454
SPT(16)	1268549702679764467	0 22 36 70 100 114 124 190 216 282 292 306 336 370 384 406	-1031342178790
SPT(16)	1268549933277807073	0 34 36 60 64 76 78 106 108 136 138 150 154 178 180 214	-800744136184
SPT(16)	1268550668576933639	0 30 44 104 132 134 162 170 174 182 210 212 240 300 314 344	-65445009618
SPT(16)	1268550745263533863	0 24 36 40 54 120 138 196 228 286 304 370 384 388 400 424	11241590606
STPT(10)	1268551277340156779	0 2 12 14 30 32 48 50 60 62	543318213522
SPT(16)	1268551278635032309	0 4 22 82 114 142 154 168 334 348 360 388 420 480 498 502	544613089052
STPT(10)	1268551310732617907	0 2 30 32 72 74 114 116 144 146	576710674650
STPT(12)	1268551460110190747	0 2 12 14 30 32 54 56 72 74 84 86	726088247490