====== 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 moduli'' for 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