Prime p₀= 1123096988683490759 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 88 2 88 2 28 2 (?)
a_n: 0 2 30 32 120 122 210 212 240 242
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: 242
Found by: crashtech
db: batch=76, k=10, 2 28 2 88 2

STPT(10)	1123093876339682237	0 2 12 14 72 74 132 134 144 146	-3112343808522
STPT(10)	1123094502977083361	0 2 6 8 48 50 90 92 96 98	-2485706407398
SPT(18)	1123094836099420927	0 30 42 52 72 94 100 114 144 190 220 234 240 262 282 292 304 334	-2152584069832
STPT(10)	1123094963483983667	0 2 60 62 102 104 144 146 204 206	-2025199507092
TPT(14)	1123095383790123827	0 2 42 44 54 56 72 74 114 116 150 152 180 182	-1604893366932
SPT(16)	1123096535711046829	0 18 30 100 108 130 142 192 220 270 282 304 312 382 394 412	-452972443930
STPT(10)	1123097173234896149	0 2 12 14 90 92 168 170 180 182	184551405390
SPT(16)	1123097203527841901	0 6 20 30 32 42 56 80 168 192 206 216 218 228 242 248	214844351142
STPT(10)	1123097391118394357	0 2 12 14 42 44 72 74 84 86	402434903598
SPT(16)	1123097426642167367	0 2 42 84 150 164 174 222 242 290 300 314 380 422 462 464	437958676608
SPT(16)	1123097482693242097	0 46 54 60 72 112 174 184 252 262 324 364 376 382 390 436	494009751338