<p>Find the sum of all prime numbers between <img alt="$1$" height="14" src="https://latex.artofproblemsolving.com/d/c/e/dce34f4dfb2406144304ad0d6106c5382ddd1446.png" width="11" /> and <img alt="$100$" height="14" src="https://latex.artofproblemsolving.com/e/5/9/e59e2c6e83eb78cca610a5fd4070ae01c8d4ae60.png" width="29" /> that are simultaneously <img alt="$1$" height="14" src="https://latex.artofproblemsolving.com/d/c/e/dce34f4dfb2406144304ad0d6106c5382ddd1446.png" width="11" /> greater than a multiple of <img alt="$4$" height="14" src="https://latex.artofproblemsolving.com/c/7/c/c7cab1a05e1e0c1d51a6a219d96577a16b7abf9d.png" width="11" /> and <img alt="$1$" height="14" src="https://latex.artofproblemsolving.com/d/c/e/dce34f4dfb2406144304ad0d6106c5382ddd1446.png" width="11" /> less than a multiple of <img alt="$5$" height="14" src="https://latex.artofproblemsolving.com/7/9/0/79069377f91364c2f87a64e5f9f562a091c8a6c1.png" width="11" />.</p> <p><img alt="$\mathrm{(A) \ } 118 \qquad \mathrm{(B) \ }137 \qquad \mathrm{(C) \ } 158 \qquad \mathrm{(D) \ } 187 \qquad \mathrm{(E) \ } 245$" height="18" src="https://latex.artofproblemsolving.com/8/0/2/802222ac93615044159fe8e191a84f492350690b.png" width="432" /></p>

Question No: 476

Find the sum of all prime numbers between $1$ and $100$ that are simultaneously $1$ greater than a multiple of $4$ and $1$ less than a multiple of $5$ .

$\mathrm{(A) \ } 118 \qquad \mathrm{(B) \ }137 \qquad \mathrm{(C) \ } 158 \qquad \mathrm{(D) \ } 187 \qquad \mathrm{(E) \ } 245$

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Tags: Number Theory

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