Prime p₀= 279588977281551137 starts a Symmetric tuple of 14 consecutive primes, which form 7 twin primes (STPT).
d_n: 0 2 28 2 22 2 16 2 16 2 22 2 28 2 (?)
a_n: 0 2 30 32 54 56 72 74 90 92 114 116 144 146
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 146
Found by: desktop64
db: batch=69, k=14, 2 28 2 22 2 16 2

SPT(14)	279588919663245403	0 18 40 54 70 84 100 138 154 168 184 198 220 238	-57618305734
SPT(14)	279588921442822679	0 2 20 78 102 120 132 200 212 230 254 312 330 332	-55838728458
SPT(14)	279588922185123743	0 8 26 30 36 38 44 90 96 98 104 108 126 134	-55096427394
SPT(14)	279588947060425021	0 10 40 60 88 112 138 160 186 210 238 258 288 298	-30221126116
SPT(14)	279588967446027607	0 12 36 70 82 124 154 222 252 294 306 340 364 376	-9835523530
TPT(12)	279588969783351209	0 2 18 20 78 80 120 122 198 200 252 254	-7498199928
SPT(14)	279588977281551137	0 2 30 32 54 56 72 74 90 92 114 116 144 146	0
TPT(14)	279588977281551137	0 2 30 32 54 56 72 74 90 92 114 116 144 146	0
SPT(14)	279588989614189147	0 12 34 46 54 76 124 132 180 202 210 222 244 256	12332638010
SPT(14)	279588991107736487	0 2 24 30 36 60 72 134 146 170 176 182 204 206	13826185350
SPT(14)	279589011348338353	0 28 36 78 90 126 148 168 190 226 238 280 288 316	34066787216