Prime p₀= 1245500675591786321 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: Cruncher Pete
db: batch=77, k=10, 2 34 2 40 2

SPT(16)	1245499139768481583	0 18 30 66 84 126 138 156 168 186 198 240 258 294 306 324	-1535823304738
STPT(10)	1245499336148580167	0 2 12 14 72 74 132 134 144 146	-1339443206154
SPT(16)	1245499348700095009	0 24 42 54 78 108 148 174 268 294 334 364 388 400 418 442	-1326891691312
STPT(10)	1245499505500127201	0 2 36 38 78 80 120 122 156 158	-1170091659120
SPT(16)	1245499937454816481	0 6 72 78 88 102 180 226 312 358 436 450 460 466 532 538	-738136969840
SPT(16)	1245500466989548039	0 4 28 34 48 54 70 84 124 138 154 160 174 180 204 208	-208602238282
SPT(16)	1245500695300191607	0 34 60 96 106 132 166 186 190 210 244 270 280 316 342 376	19708405286
SPT(16)	1245500728711468661	0 60 78 168 182 248 252 288 290 326 330 396 410 500 518 578	53119682340
STPT(10)	1245501040841520887	0 2 54 56 72 74 90 92 144 146	365249734566
STPT(10)	1245501245812675739	0 2 18 20 30 32 42 44 60 62	570220889418
SPT(16)	1245501699483899491	0 30 40 82 112 118 142 148 222 228 252 258 288 330 340 370	1023892113170