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 Engineering Sci Advisor HW Helper Thanks P: 7,177 You can cut down the search a lot by using modular arithmetic. All primes > 3 are equal to either 1 or 5 mod 6. 98 = 2 mod 6. The only possibilities that sum to 2 mod 6 are 1+1+1+1+5+5, 1+5+5+5+5+5, 3+1+1+1+1+1, 3+1+1+5+5+5 Consider the first option 1+1+1+1+5+5. The only sums of 4 primes equal to 1 mod 6 that are less than 98 are 7+13+19+31 = 70 7+13+19+37 = 76 7+13+19+43 = 82 So the 2 primes equal to 2 mod 6 must sum to 16, 22, or 28. The only options are 5+11=16 5+17=22 5+23=28 11+17=28 So we have 4 solutions, so far. The rest is left as an exercise for the reader.