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The primes required are:

2 = (4+4)/4

3 = (4+4+4)/4

5 = (4+4+4+4+4)/4

7 = (4*4+4+4+4)/4

11 = (4(4*4-4)-4)/4

13 = (4*(4*4-4)+4)/4

17 = (4*4*4+4)/4

19 = (4*(4*4+4)-4)/4

23 = (4*(4*4+4+4)-4)/4

29 = (4*(4*4+4+4+4)+4)/4

31 = (4*4*(4+4)-4)/4

37 = (4*4*(4+4)+4*4+4)/4

41 = (4^4-4*(4*4)+4)/4

43 = (4^4-4(4*4+4+4))/4

47 = (4^4-4*4*4-4)/4

The remainder are left as an exercise. It should be noted that most of these are impossible to express with only six fours without either defining new operators or allowing for facetious, unmathematical cheats such as allowing 44 to be used.

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12y ago

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