Prime p₀= 1235343756350540279 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 16 2 16 2 40 2 (?)
a_n: 0 2 42 44 60 62 78 80 120 122
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: 122
Found by: Cruncher Pete
db: batch=77, k=10, 2 40 2 16 2

SPT(16)	1235342902745370017	0 2 14 26 36 44 92 104 162 174 222 230 240 252 264 266	-853605170262
SPT(16)	1235342936779545031	0 6 12 42 58 88 102 118 180 196 210 240 256 286 292 298	-819570995248
SPT(16)	1235342952688986839	0 38 48 54 78 98 200 222 230 252 354 374 398 404 414 452	-803661553440
SPT(16)	1235343019102872431	0 30 42 48 50 56 72 92 126 146 162 168 170 176 188 218	-737247667848
STPT(10)	1235343037839346529	0 2 30 32 60 62 90 92 120 122	-718511193750
STPT(10)	1235343273745366127	0 2 24 26 42 44 60 62 84 86	-482605174152
STPT(10)	1235343887126969699	0 2 48 50 60 62 72 74 120 122	130776429420
SPT(16)	1235343907628979223	0 6 66 70 78 108 148 150 214 216 256 286 294 298 358 364	151278438944
SPT(18)	1235344115289821827	0 16 24 36 54 66 72 114 156 160 202 244 250 262 280 292 300 316	358939281548
STPT(10)	1235344186495593047	0 2 30 32 42 44 54 56 84 86	430145052768
STPT(10)	1235344299742924211	0 2 36 38 78 80 120 122 156 158	543392383932