If you just want to do some calculations and not heavy number crunching you can use my calculator Kalkulon together with a simple Kalkulon script for big number arithmetic. An interactive Kalkulon session looks like this:

Load("examples/bignum.k")
                    outl[1] = 0

string2Bn("1234567890ABCDEFGHIJKLMNOPQRSTU",31)
                    outl[2] = {587, 938220, 58035, 844882, 441786, 886253, 755598, 800665}

string2Bn("UTSR",31)
                    outl[3] = {922494}

mulBn(outl[2], outl[3])
                    outl[4] = {542, 369480, 374217, 718688, 983253, 751847, 772017, 360020, 658510}

printBn(out)
542369480374217718688983253751847772017360020658510
                    outl[5] = 51

Bn2string(outl[4],31)
                    outl[6] = "121UOIC5UEHLRAUOIC5UOIC5UOIC5UNHB64"

divBn(outl[4], outl[2])
                    outl[7] = {922494}

Bn2string(out,31)
                    outl[8] = "UTSR"

I am just curious: why do you want to calculate in base 31?