5*(105-1)/9 + 4*104 + 4*102 + 4
Using Pari/gp (< 1s)
     gp > isprime(5*(10^5-1)/9+4*10^4+4*10^2+4)
     %1 = 1


5*(1079-1)/9 + 4*1078 + 4*1039 + 4
Using Pari/gp (< 1s)
     gp > isprime(5*(10^79-1)/9+4*10^78+4*10^39+4)
     %1 = 1


5*(10349-1)/9 + 4*10348 + 4*10174 + 4
Using Pari/gp (time = 2,422 ms)
     gp > default(parisizemax,"1G")
     gp > isprime(5*(10^349-1)/9+4*10^348+4*10^174+4)
     %1 = 1


5*(102989-1)/9 + 4*102988 + 4*101494 + 4
Proven by certificate by Anonymous (November 20, 2022)
http://factordb.com/index.php?id=1100000002732286243


5*(1045983-1)/9 + 4*1045982 + 4*1022991 + 4
C:\pfgw>pfgw64 -q"5*(10^45983–1)/9+4*10^45982+4*10^22991+4"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

5*(10^45983–1)/9+4*10^45982+4*10^22991+4 is 3-PRP! (11.9099s+0.0008s)
 

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