Verifying the uniqueness of a linear congruent generator for user identifiers

Question

Verifying the uniqueness of a linear congruent generator for user identifiers

ID Requirements:

Short (# characters for user input)
Allow as many identifiers as possible
Seems random (so no one can easily guess the count of users by id)
No mixed code characters (easier for user)
No abusive words

So, I decided to go with an uppercase string with 6 characters, without vowels, created by a linear congruent generator ordered by user account. I learned about LCG from the wiki, and I would like to verify that my code is correct, since I myself compiled the coefficients in the LCG and would not want there to be a clash of identifiers. I myself tried to test for collisions, but I ran out of the heap of space while storing identifiers on the map after 2 million. I think that mathematics checks, but really appreciates the second (or thousand) set of eyes. (Also, this is actually not the case with JS, so if there is a more efficient way to replace vowels, I would like to know).

// UserId generated from stored userCount key in redis, sequenced by a Linear
// Congruental generator, and stringified with a radix of 31 (all numbers and
// letters besides vowels = 10 + 26 - 5 = 31).
//
// The equation we will use to generate the sequence is:
// userVal = (a * userCount + c) % m + minVal

// To guarantee each userId is at least 6 characters, we need:
// minVal = 31^5 = 28629151
//
// To guarantee that our userId is at most 6 characters, we need:
// log31(minVal + maxVal + 1) = 6
// => 31^6 = minVal + maxVal + 1
// => maxVal = 31^6 - minVal - 1 = 858874529
//
// So our LCG needs to have:
// 1) m < maxVal
// 2) m and c relatively prime
// 3) a-1 is divisible by 4 if m is
// 4) a-1 is divisible by all prime factors of m
//
// m = 858062848 = 2^16 * 13093
// c = 1
// a = 3351809 = 2^8 * 13093 + 1
//
// This means we can support 858062848 unique userIds (>850 million).
// If we ever cross that amount, it will be a good problem to solve :)
this.getUserId = function(){
    var userCount = Spark.getRedis().incr("unique-id:user");

    var a = 3351809;
    var c = 1;
    var m = 858062848;
    var minVal = 28629151;

    var userVal = (a * userCount + c) % m + minVal;

    return userVal.toString(31)
        .toUpperCase()
        .replace(/A/g, 'V')
        .replace(/E/g, 'W')
        .replace(/I/g, 'X')
        .replace(/O/g, 'Y')
        .replace(/U/g, 'Z');
};