Prime p₀= 3679926577199592677 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 28 2 28 2 40 2 (?)
a_n: 0 2 42 44 72 74 102 104 144 146
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: 146
Found by: [SG]KidDoesCrunch
db: batch=84, k=10, 2 40 2 28 2

SPT(16)	3679923994705209863	0 8 30 44 68 86 108 140 204 236 258 276 300 314 336 344	-2582494382814
SPT(13)	3679924313694048481	0 12 18 42 48 78 90 102 132 138 162 168 180	-2263505544196
STPT(10)	3679924637616254717	0 2 30 32 42 44 54 56 84 86	-1939583337960
STPT(10)	3679924773595962251	0 2 6 8 48 50 90 92 96 98	-1803603630426
SPT(16)	3679925236327475671	0 42 46 106 112 172 180 250 372 442 450 510 516 576 580 622	-1340872117006
SPT(22)	3679925707617846839	0 8 14 50 54 78 80 92 98 102 104 138 140 144 150 162 164 188 192 228 234 242	-869581745838
STPT(10)	3679926610806797621	0 2 6 8 48 50 90 92 96 98	33607204944
STPT(10)	3679926798898771229	0 2 48 50 90 92 132 134 180 182	221699178552
SPT(16)	3679927162537506971	0 30 98 126 128 132 146 206 282 342 356 360 362 390 458 488	585337914294
STPT(10)	3679927475856896321	0 2 36 38 78 80 120 122 156 158	898657303644
SPT(16)	3679927644287944789	0 24 48 64 90 94 108 148 180 220 234 238 264 280 304 328	1067088352112