Prime p₀= 4044972127394292509 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 10 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 42 44 60 62
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: 62
Found by: Centaur
db: batch=84, k=10, 2 16 2 10 2

SPT(16)	4044970971700274437	0 24 30 40 54 84 136 142 174 180 232 262 276 286 292 316	-1155694018072
STPT(10)	4044971188595378159	0 2 18 20 30 32 42 44 60 62	-938798914350
SPT(16)	4044971404587784933	0 28 36 78 150 190 196 210 226 240 246 286 358 400 408 436	-722806507576
SPT(16)	4044971426549695189	0 10 28 72 168 172 198 300 382 484 510 514 610 654 672 682	-700844597320
STPT(10)	4044971479873036091	0 2 36 38 78 80 120 122 156 158	-647521256418
STPT(10)	4044971782300463681	0 2 6 8 18 20 30 32 36 38	-345093828828
STPT(10)	4044972147730481657	0 2 30 32 42 44 54 56 84 86	20336189148
SPT(16)	4044972250643813891	0 20 30 36 42 62 132 140 168 176 246 266 272 278 288 308	123249521382
SPT(16)	4044972482343271177	0 40 70 90 114 156 184 222 244 282 310 352 376 396 426 466	354948978668
STPT(10)	4044972649440038747	0 2 54 56 72 74 90 92 144 146	522045746238
SPT(16)	4044973116456508927	0 10 12 70 106 132 136 162 220 246 250 276 312 370 372 382	989062216418