# Is generating a large random number more unique than generating each digit in that number?

I'm using a PRNG (PHP's default `rand()` implementation) to generate unique 16 digit numbers. Does it make sense to generate digits one by one, or the number at once?

I'm using PHP.

• It depends upon the actual implementation and system. Dec 1, 2014 at 12:13
• Generating digit by digit is a significant extra effort (primarily for you) and another source of potential bugs. So unless generating digit by digit actually results in higher quality numbers (which you don't seem to believe either, from the phrasing of the title), no it does not make sense.
– user7043
Dec 1, 2014 at 12:16
• @delnan, this is my question exactly. I don't know what's better. I had a feeling that generating one by one would be bad since i would be basically generating sequences of numbers and PRNGs use previous number to generate a new number. But i can't really prove it. Dec 1, 2014 at 12:41
• @Oleg If number generation is dependant on the previous number, then generating one by one is a very bad idea. There would only be 2^32 * 10 unique values (if the seed is 32 bits), instead of the ~2^53 possible 16-digit numbers. Dec 1, 2014 at 13:04
• In general it will be a lot slower and you will still have all the problems of the underlying PRNG. What exactly do you mean by "more unique" anyway? Is it predictability? Closer to a HRNG? Collisions if used as an UID generator? Dec 1, 2014 at 13:24

In principle each arithmetic pseudo-random number generator (such as PHP's) has a finite period after which the same sequence of numbers will repeat. And most generators will generate a fixed minimum number of bits (often 32) for you internally at each step, no matter how large or small the range of results is that you asked for.

So generating each digit separately will eat up the sequence of your generator more quickly and thus make the resulting sequence of complete numbers less 'random' overall.

In practice the most relevant difference is probably that generating each digit separately is a lot more work.

Both of these effects, however, point in the same direction: You should generate your whole random number at once.

With a PRNG that has equal probability for "single decimal digits" as well as "16-digit decimal numbers", no, they should be equal.

However, the PRNG is unlikely to have perfect probability for base-10 numbers, so "possibly". It would depend on how much this influences the probabiity for any specific digit.

Bear in mind that a 16-digit number is up to 54 bits, so this may influence your decision as to if you should generate you number in pieces or not.