Prime p₀= 3588417641922196211 starts a Symmetric tuple of 22 consecutive primes (SPT).
d_n: 0 90 60 26 52 20 4 6 14 10 36 32 36 10 14 6 4 20 52 26 60 90 (?)
a_n: 0 90 150 176 228 248 252 258 272 282 318 350 386 396 410 416 420 440 492 518 578 668
All 22 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 668
Found by: [SG]KidDoesCrunch
db: batch=84, k=22, 90 60 26 52 20 4 6 14 10 36 32

SPT(16)	3588415292091490327	0 10 22 52 60 70 84 124 192 232 246 256 264 294 306 316	-2349830705884
SPT(16)	3588415353910580833	0 40 78 118 120 138 148 160 324 336 346 364 366 406 444 484	-2288011615378
SPT(16)	3588416163185309707	0 10 70 84 94 114 142 186 220 264 292 312 322 336 396 406	-1478736886504
SPT(16)	3588416670878033431	0 10 12 48 90 106 112 132 196 216 222 238 280 316 318 328	-971044162780
SPT(16)	3588416885304447667	0 66 84 106 160 184 210 216 220 226 252 276 330 352 370 436	-756617748544
SPT(16)	3588417303572741609	0 8 14 50 68 74 84 92 120 128 138 144 162 198 204 212	-338349454602
TPT(14)	3588417965171067797	0 2 30 32 72 74 84 86 114 116 222 224 240 242	323248871586
SPT(16)	3588418427973545059	0 10 18 34 84 150 190 244 264 318 358 424 474 490 498 508	786051348848
STPT(10)	3588418744004398919	0 2 18 20 30 32 42 44 60 62	1102082202708
STPT(10)	3588418769742685997	0 2 30 32 42 44 54 56 84 86	1127820489786
SPT(16)	3588418893081010159	0 34 72 100 120 190 198 204 238 244 252 322 342 370 408 442	1251158813948