There are multiple valid combinations, given these clues:

7275, 7419, 7536, 7579, 7678, 7849, 7876, 8529, 8547, 8565, 8789, 8987, 9297, 9495, 9594

for example, 7275:

• 7+2+7+5 = 21, 72 - 75 = -21. 21 > -21
• 727*5 + 7+2+7+5 = 511, evenly divisible by 7, but not 2 or 5
• being divisible by 7, it's trivially non-prime
• 7 > 6

and 7419:

• 7+4+1+9 = 21. 74 - 19 = 19. 21 > 19
• 741*9 + 7+4+1+9 = 273. divisible by 7 and 1, but not 9 or 4.
• being divisible by 7, it's trivially non-prime
• 7 > 6.

Methodology is pretty simple. for all numbers 0000-9999, have a computer check if it matches all conditions.

Also, an unstated assumption of your question is that digits are all non-zero. Otherwise, the second clue isn't really defined.

edited to match intended question:

given that the number is prime, the only potentially valid combination is 8017.

8017:

• 8+0+1+7 = 16, 80 - 17 = -7, 16 > -7
• 801*7 + 8+0+1+7 = 16, divisible by 8 and 1, but not 7. 0 is undefined.
• 8017 is prime.
• 8 > 6.

This depends on the assumption that 0 does not divide 16 evenly, which depends on your definition. This can go either way - 16/0 is undefined, so you could say that (0 divides 16) is undefined. Or, since there's no m such that m*0 = 16, you could say that (0 divides 16) is false.

Methodology is pretty simple. for all numbers 0000-9999, have a computer check if it matches all conditions.