Flicka three was amazing, they keep getting better and better. I have no solid proof, but I have read that there is a high probability that there will be another Flicka. :)
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4 +4+4+4+4+4+4+4+4=40
(4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4) ÷ 4 = 27
Sure, using the number 4 four times, you can create the numbers 1 to 20 as follows: 1 = 4 / 4 + 4 - 4 2 = 4 / 4 + 4 / 4 3 = 4 - 4 / 4 + 4 4 = 4 + 4 - 4 - 4 5 = 4 + 4 / 4 6 = 4 + 4 - 4 / 4 7 = 4 + 4 / 4 + 4 8 = 4 + 4 + 4 / 4 9 = (4 + 4) / (4 / 4) 10 = 4 + 4 + 4 - 4 11 = 4 + 4 + 4 / 4 12 = 4 + 4 + 4 + 4 13 = (4 + 4) / 4 + 4 14 = 4 * 4 - 4 / 4 15 = 4 + 4 + 4 + 4 - 4 16 = 4 * 4 - 4 + 4 17 = 4 * 4 + 4 / 4 18 = (4 + 4) * (4 - 4) 19 = 4 * 4 + 4 - 4 20 = 4 * 4 + 4 / 4
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.
1 = 44 / 442 = 4 * 4 / (4 + 4)3 = (4 + 4 + 4) / 44 = 4 + (4 * (4 - 4))5 = (4 + (4 * 4)) / 46 = 4 + ((4 + 4) / 4)7 = (44 / 4) - 48 = 4 + 4 + 4 - 49 = 4 + 4 + (4 / 4)10 = (44 - 4) / 411 = (4 / 4) + (4 / .4)12 = (4 + 44) / 413 = 4 + ((4 - .4) / .4)14 = (4 * (4 - .4)) - .415 = 4 + (44 / 4)16 = (44 - 4) * .417 = (4 * 4) + (4 / 4)18 = (44 * .4) + .419 = (4 + 4 - .4) / .420 = 4 * (4 + (4 / 4))