Generate Large Prime Factors
Simple Linux commands to generate large prime factors
- Generate prime Candidates
ssh-keygen -G candidates -b 2048
- Note:
- Use 1024 (or lesser) for faster and smaller prime number candidates generation, instead of 2048
- 256 bit is considered uncrackable in 2023.
- Creates a file called candidates in current directory
- Find prime from candidates
ssh-keygen -T moduli -f candidates
- Creates a file called moduli in current directory, taking input from the candidates file
- Pick two primes from moduli file - this is last column in each row (the longest number)
- Refer to
man modulifor details on other columns - Set two variables with primes, PRIME1 and PRIME2 for next step to create a PRODUCT
- Create a product
export BC_LINE_LENGTH=0
echo "obase=16;ibase=16;$PRIME1*$PRIME2"|bc
OR
PRODUCT=$(echo "obase=16;ibase=16;$PRIME1*$PRIME2"|bc)
- Optionally convert Hex to Decimal
echo "obase=10; ibase=16; $PRODUCT" | bc
Other suggestions
- Generate multiple candidates/moduli files with different bit size and make prime factors out of them for security
Example Primes
Output of moduli file, candidates generated with 512 bits. Last long column is prime in hex.
20231229143039 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC3F850A7 20231229143039 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC3FA65B7 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC3FDC6CB 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC3FE2B63 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC3FFCE13 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC4081F83 20231229143040 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC4095087 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC4104E73 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC413848B 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC4165713 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC4198B63 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC419B21B 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC41A265B 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC41C8FE3 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC41F125B 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC423E95B 20231229143040 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC424C7C7 20231229143040 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC4250EA7 20231229143040 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC42583D7 20231229143040 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC425F2D7 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC427D493 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC42C1CFB 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC42E4E73 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC435B943 20231229143040 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC437BD37 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC438673B 20231229143040 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC43A07B7 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC43D8D2B 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC44C1EBB 20231229143040 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC455752B 20231229143040 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC456A197 20231229143041 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC45BA2AF 20231229143041 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC46755AB 20231229143041 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC468E1AB 20231229143041 2 6 100 511 2 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC468FB2B 20231229143041 2 6 100 511 5 F32AF1CDB1EE0CCBAFEC309C4861D9EFA7EF464F76F53338C1980C99E8777C4FB844031A54F85BA01527773BDFD52872468F17250C2F7383988794DAC4727877
Another set
20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E27FF388A3 20231229145001 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E27FF75F5F 20231229145001 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E27FFB6EAF 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E27FFE5973 20231229145001 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2800055E7 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28002FE63 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28006DAE3 20231229145001 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2800894AF 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2800C61AB 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28012DFC3 20231229145001 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E280181AD7 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2801AA5FB 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2801F48F3 20231229145001 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28020095F 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28022C2BB 20231229145001 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28024B8FF 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28027EC83 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2802C6AEB 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2802D1D53 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2802FC233 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E280306BFB 20231229145001 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2803252EB 20231229145002 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28033E41F 20231229145002 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28034207F 20231229145002 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28037C63F 20231229145002 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E280410D67 20231229145002 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E280413B03 20231229145002 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28041FBFF 20231229145002 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E280437EB7 20231229145002 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28044C137 20231229145002 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28045F2FB 20231229145002 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2804777AB 20231229145002 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28047D74B 20231229145002 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2804AAF1F 20231229145002 2 6 100 511 5 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2804C7BCF 20231229145002 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E28058C73B 20231229145002 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2805AD5A3 20231229145002 2 6 100 511 2 D6D2B689F1F16684A8EECF2A5266D18A744EFD5ADF666E37BE830FCAA39A83A0B963BB999997644688C86F06372E4B3801B6C7F7FD345BD3F0EF16E2806B31D3
