Prime p₀= 2678444123889441371 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 34 2 40 2 40 2 34 2 (?)
a_n: 0 2 36 38 78 80 120 122 156 158
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: 158
Found by: [SG-FC] hl
db: batch=82, k=10, 2 34 2 40 2

SPT(16)	2678442908319199267	0 36 54 60 120 156 166 210 310 354 364 400 460 466 484 520	-1215570242104
STPT(10)	2678443132415854589	0 2 42 44 60 62 78 80 120 122	-991473586782
SPT(16)	2678443507445368937	0 32 36 60 84 92 110 126 170 186 204 212 236 260 264 296	-616444072434
SPT(16)	2678443687618529849	0 18 20 32 74 78 104 120 152 168 194 198 240 252 254 272	-436270911522
SPT(16)	2678443974938452507	0 12 30 40 52 66 96 120 142 166 196 210 222 232 250 262	-148950988864
SPT(16)	2678444069394378547	0 10 66 72 114 142 174 262 264 352 384 412 454 460 516 526	-54495062824
SPT(16)	2678444235229116677	0 26 44 56 92 102 114 182 264 332 344 354 390 402 420 446	111339675306
SPT(16)	2678444373499197547	0 10 46 70 96 124 126 136 144 154 156 184 210 234 270 280	249609756176
SPT(13)	2678444797475921141	0 6 42 72 90 120 126 132 162 180 210 246 252	673586479770
STPT(10)	2678444983522747469	0 2 18 20 30 32 42 44 60 62	859633306098
SPT(16)	2678445091694604461	0 8 20 26 42 48 56 78 80 102 110 116 132 138 150 158	967805163090