Prime p₀= 4408798575422706401 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 26 4 18 32 16 2 40 2 40 2 16 32 18 4 26 (?)
a_n: 0 26 30 48 80 96 98 138 140 180 182 198 230 248 252 278
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 278
Found by: [SG]KidDoesCrunch
db: batch=85, k=16, 26 4 18 32 16 2 40 2

SPT(16)	4408796606771303963	0 30 84 86 104 126 144 150 164 170 188 210 228 230 284 314	-1968651402438
SPT(16)	4408796936600339341	0 36 66 70 88 90 132 192 196 256 298 300 318 322 352 388	-1638822367060
TPT(14)	4408797416335163141	0 2 36 38 78 80 90 92 108 110 120 122 336 338	-1159087543260
SPT(18)	4408797436464555271	0 12 16 46 90 96 130 132 142 186 196 198 232 238 282 312 316 328	-1138958151130
STPT(10)	4408797535192206197	0 2 30 32 42 44 54 56 84 86	-1040230500204
SPT(16)	4408798536619026071	0 20 26 30 42 68 90 92 216 218 240 266 278 282 288 308	-38803680330
STPT(10)	4408798729874306237	0 2 30 32 42 44 54 56 84 86	154451599836
SPT(16)	4408799155753274531	0 30 32 42 60 90 132 140 162 170 212 242 260 270 272 302	580330568130
STPT(14)	4408800087746779367	0 2 24 26 30 32 42 44 54 56 60 62 84 86	1512324072966
TPT(14)	4408800087746779367	0 2 24 26 30 32 42 44 54 56 60 62 84 86	1512324072966
SPT(16)	4408800257634305531	0 8 18 20 26 38 66 126 242 302 330 342 348 350 360 368	1682211599130