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


5*(107-1)/9 - 2*106 - 2*103 - 2
Using Pari/gp (< 1s)
     gp > isprime(5*(10^7-1)/9-2*10^6-2*10^3-2)
     %1 = 1


5*(1037-1)/9 - 2*1036 - 2*1018 - 2
Using Pari/gp (< 1s)
     gp > isprime(5*(10^37-1)/9-2*10^36-2*10^18-2)
     %1 = 1


5*(1043-1)/9 - 2*1042 - 2*1021 - 2
Using Pari/gp (< 1s)
     gp > isprime(5*(10^43-1)/9-2*10^42-2*10^21-2)
     %1 = 1


5*(1055-1)/9 - 2*1054 - 2*1027 - 2
Using Pari/gp (< 1s)
     gp > isprime(5*(10^55-1)/9-2*10^54-2*10^27-2)
     %1 = 1


5*(10317-1)/9 - 2*10316 - 2*10158 - 2
Using Pari/gp (time = 1,141 ms)
     gp > isprime(5*(10^317-1)/9-2*10^316-2*10^158-2)
     %1 = 1


5*(101231-1)/9 - 2*101230 - 2*10615 - 2
Proven by certificate by Anonymous (August 22, 2022)
http://factordb.com/index.php?id=1100000003850484513


5*(101669-1)/9 - 2*101668 - 2*10834 - 2
Proven by certificate by Anonymous (January 24, 2023)
http://factordb.com/index.php?id=1100000004282690320 (Certificate)


5*(106725-1)/9 - 2*106724 - 2*103362 - 2
C:\pfgw>pfgw64 -q"5*(10^6725-1)/9-2*10^6724-2*10^3362-2"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

5*(10^6725-1)/9-2*10^6724-2*10^3362-2 is 3-PRP! (0.4494s+0.0007s)


5*(107265-1)/9 - 2*107264 - 2*103632 - 2
C:\pfgw>pfgw64 -q"5*(10^7265-1)/9-2*10^7264-2*10^3632-2"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

5*(10^7265-1)/9-2*10^7264-2*10^3632-2 is 3-PRP! (0.4877s+0.0007s)


5*(107691-1)/9 - 2*107690 - 2*103845 - 2
C:\pfgw>pfgw64 -q"5*(10^7691-1)/9-2*10^7690-2*10^3845-2"
PFGW Version 4.0.4.64BIT.20221214.Win_Dev [GWNUM 30.11]

5*(10^7691-1)/9-2*10^7690-2*10^3845-2 is 3-PRP! (0.5170s+0.0007s)
 

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Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com