How to generate random 64-bit unsigned integer in C

Concerning "So results are always 18 digits or 20 digits."

See @Thomas comment. If you generate random numbers long enough, code will create ones like 5, 11 and 33387. If code generates 1,000,000,000 numbers/second, it may take a year as very small numbers < 100,000 are so rare amongst all 64-bit numbers.

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rand() simple returns random bits. A simplistic method pulls 1 bit at a time

uint64_t rand_uint64_slow(void) {
  uint64_t r = 0;
  for (int i=0; i<64; i++) {
    r = r*2 + rand()%2;
  }
  return r;
}

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Assuming RAND_MAX is some power of 2 - 1 as in OP's case 1073741823 == 0x3FFFFFFF, take advantage that 30 at least 15 bits are generated each time. The following code will call rand() 5 3 times - a tad wasteful. Instead bits shifted out could be saved for the next random number, but that brings in other issues. Leave that for another day.

uint64_t rand_uint64(void) {
  uint64_t r = 0;
  for (int i=0; i<64; i += 15 /*30*/) {
    r = r*((uint64_t)RAND_MAX + 1) + rand();
  }
  return r;
}

A portable loop count method avoids the 15 /*30*/ - But see 2020 edit below.

#if RAND_MAX/256 >= 0xFFFFFFFFFFFFFF
  #define LOOP_COUNT 1
#elif RAND_MAX/256 >= 0xFFFFFF
  #define LOOP_COUNT 2
#elif RAND_MAX/256 >= 0x3FFFF
  #define LOOP_COUNT 3
#elif RAND_MAX/256 >= 0x1FF
  #define LOOP_COUNT 4
#else
  #define LOOP_COUNT 5
#endif

uint64_t rand_uint64(void) {
  uint64_t r = 0;
  for (int i=LOOP_COUNT; i > 0; i--) {
    r = r*(RAND_MAX + (uint64_t)1) + rand();
  }
  return r;
}

The autocorrelation effects commented here are caused by a weak rand(). C does not specify a particular method of random number generation. The above relies on rand() - or whatever base random function employed - being good.

If rand() is sub-par, then code should use other generators. Yet one can still use this approach to build up larger random numbers.

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[Edit 2020]

Hallvard B. Furuseth provides as nice way to determine the number of bits in RAND_MAX when it is a Mersenne Number - a power of 2 minus 1.

#define IMAX_BITS(m) ((m)/((m)%255+1) / 255%255*8 + 7-86/((m)%255+12))
#define RAND_MAX_WIDTH IMAX_BITS(RAND_MAX)
_Static_assert((RAND_MAX & (RAND_MAX + 1u)) == 0, "RAND_MAX not a Mersenne number");

uint64_t rand64(void) {
  uint64_t r = 0;
  for (int i = 0; i < 64; i += RAND_MAX_WIDTH) {
    r <<= RAND_MAX_WIDTH;
    r ^= (unsigned) rand();
  }
  return r;
}

If you don't need cryptographically secure pseudo random numbers, I would suggest using MT19937-64. It is a 64 bit version of Mersenne Twister PRNG.

Please, do not combine rand() outputs and do not build upon other tricks. Use existing implementation:

http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt64.html