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Gerry Myerson
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For consecutive primes a<b<c$a\lt b\lt c$, prove that a+b>=c$a+b\ge c$.

For consecutive primes $a\lt b\lt c$, prove that $a+b\ge c$.

I cannot find a counter-example to this. Do we know if this inequality is true? Alternatively, is this some documented problem (solved or unsolved)?

For consecutive primes a<b<c, prove that a+b>=c.

I cannot find a counter-example to this. Do we know if this inequality is true? Alternatively, is this some documented problem (solved or unsolved)?

For consecutive primes $a\lt b\lt c$, prove that $a+b\ge c$.

For consecutive primes $a\lt b\lt c$, prove that $a+b\ge c$.

I cannot find a counter-example to this. Do we know if this inequality is true? Alternatively, is this some documented problem (solved or unsolved)?

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Bavid
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For consecutive primes a<b<c, prove that a+b>=c.

I cannot find a counter-example to this. Do we know if this inequality is true? Alternatively, is this some documented problem (solved or unsolved)?