Prime p₀= 1028079307082542457 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 84 86
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: 86
Found by: Theadalus
db: batch=76, k=10, 2 10 2 28 2

TPT(14)	1028078316782037977	0 2 30 32 120 122 150 152 210 212 234 236 330 332	-990300504480
STPT(10)	1028078461702737407	0 2 30 32 42 44 54 56 84 86	-845379805050
SPT(18)	1028078647065828529	0 10 12 40 42 48 108 132 162 208 238 262 322 328 330 358 360 370	-660016713928
SPT(16)	1028078981759172197	0 2 24 32 44 156 176 194 252 270 290 402 414 422 444 446	-325323370260
SPT(16)	1028079007474434931	0 12 22 78 126 156 190 198 400 408 442 472 520 576 586 598	-299608107526
STPT(10)	1028079015928373579	0 2 42 44 60 62 78 80 120 122	-291154168878
SPT(16)	1028079311048023681	0 10 16 18 52 72 82 96 142 156 166 186 220 222 228 238	3965481224
STPT(10)	1028079404937885329	0 2 78 80 120 122 162 164 240 242	97855342872
STPT(10)	1028079555923178257	0 2 30 32 72 74 114 116 144 146	248840635800
STPT(10)	1028079591258579029	0 2 18 20 60 62 102 104 120 122	284176036572
SPT(16)	1028079647547915769	0 4 72 102 112 118 148 174 478 504 534 540 550 580 648 652	340465373312