There are an infinite amount of numbers that have a greater difference than 1,000
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431 and 669.
Only 1 pair of prime numbers, 2 and 5, have a difference of 3. All prime numbers greater than 2 are odd so will have an even difference.
500
-- write the difference between the numbers without regard for their signs -- give the difference the same sign as the original number with the greater size
It's not true. 500 could round to 1000. 1499 could as well. Their difference is greater than 499.