Prime p₀= 1296942767960345711 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: Cruncher Pete
db: batch=77, k=10, 2 4 2 10 2

SPT(16)	1296941098189070813	0 6 50 66 98 150 164 168 176 180 194 246 278 294 338 344	-1669771274898
STPT(10)	1296941272267413401	0 2 156 158 168 170 180 182 336 338	-1495692932310
STPT(10)	1296941358960677387	0 2 42 44 72 74 102 104 144 146	-1408999668324
STPT(10)	1296941493767636747	0 2 30 32 60 62 90 92 120 122	-1274192708964
STPT(10)	1296941752554194207	0 2 24 26 42 44 60 62 84 86	-1015406151504
SPT(16)	1296942199243457827	0 34 40 42 90 100 124 126 130 132 156 166 214 216 222 256	-568716887884
SPT(16)	1296943310493396793	0 34 36 40 64 78 100 106 168 174 196 210 234 238 240 274	542533051082
SPT(16)	1296943441131623459	0 48 104 122 152 158 174 198 224 248 264 270 300 318 374 422	673171277748
SPT(16)	1296943712412769207	0 76 96 120 174 180 190 222 274 306 316 322 376 400 420 496	944452423496
STPT(10)	1296944617637307599	0 2 42 44 120 122 198 200 240 242	1849676961888
STPT(10)	1296944733472184021	0 2 36 38 78 80 120 122 156 158	1965511838310