Prime p₀= 2044738087211647769 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 16 2 70 2 28 2 34 2 28 2 (?)
a_n: 0 2 12 14 30 32 102 104 132 134 168 170 198 200
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 200
Found by: Landjunge
db: batch=80, k=14, 10 16 70 28 34 28

SPT(16)	2044736595010860241	0 22 58 106 142 156 162 208 270 316 322 336 372 420 456 478	-1492200787528
STPT(10)	2044736897516950067	0 2 12 14 72 74 132 134 144 146	-1189694697702
SPT(16)	2044737600324922577	0 2 6 32 42 74 116 152 204 240 282 314 324 350 354 356	-486886725192
STPT(10)	2044737682995917051	0 2 6 8 18 20 30 32 36 38	-404215730718
STPT(10)	2044737821258258051	0 2 30 32 78 80 126 128 156 158	-265953389718
STPT(10)	2044737889881082211	0 2 6 8 48 50 90 92 96 98	-197330565558
STPT(10)	2044738196020981337	0 2 30 32 60 62 90 92 120 122	108809333568
SPT(16)	2044738371999202697	0 6 80 96 104 122 212 236 270 294 384 402 410 426 500 506	284787554928
SPT(16)	2044738671684070721	0 42 66 90 116 242 258 276 332 350 366 492 518 542 566 608	584472422952
SPT(16)	2044738677698612471	0 2 78 92 98 120 140 156 212 228 248 270 276 290 366 368	590486964702
SPT(16)	2044739045131249279	0 40 42 72 82 112 138 142 168 172 198 228 238 268 270 310	957919601510