This problem came in NMTC 2015. The prime numbers must be less than 54. Listing first few possibilities 53 and 1, 52 and 2, 51 and 3, 50 and 4, 49 and 5, 48 and 6, 47 and 7. Only the pair 47 and 7 are both primes and 47 is the biggest.
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Svatejas Shivakumar
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6 months, 3 weeks ago

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@Svatejas Shivakumar
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You seem to be assuming there are only two prime numbers, when the question doesn't explicitly state that.

Otherwise, there can be other solutions like \( (3,7,71) \)
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Siddhartha Srivastava
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6 months, 3 weeks ago

@Ayush Rai
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Nope. Pair wise distinct does not mean only two. Pair wise distinct means that given a set of elements, no two elements (pair) of the set are the same. It does not restrict the number of elements in the set.

https://proofwiki.org/wiki/Definition:Distinct/Plural/Pairwise_Distinct
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Siddhartha Srivastava
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6 months, 3 weeks ago

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@Siddhartha Srivastava
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definition:A set of objects is pairwise distinct if each pair of elements of that set is distinct.
It clearly states a pair of elements which means two elements.
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Ayush Rai
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6 months, 3 weeks ago

@Ayush Rai
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You can check the top comment here or this. Notice how none of them refer to only two elements when talking about pairwise distinct elements.
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Siddhartha Srivastava
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6 months, 3 weeks ago

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TopNewestThis problem came in NMTC 2015. The prime numbers must be less than 54. Listing first few possibilities 53 and 1, 52 and 2, 51 and 3, 50 and 4, 49 and 5, 48 and 6, 47 and 7. Only the pair 47 and 7 are both primes and 47 is the biggest. – Svatejas Shivakumar · 6 months, 3 weeks ago

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Otherwise, there can be other solutions like \( (3,7,71) \) – Siddhartha Srivastava · 6 months, 3 weeks ago

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– Ayush Rai · 6 months, 3 weeks ago

It clearly states pair wise that means only two prime numbers.Log in to reply

https://proofwiki.org/wiki/Definition:Distinct/Plural/Pairwise_Distinct – Siddhartha Srivastava · 6 months, 3 weeks ago

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It clearly states a pair of elements which means two elements. – Ayush Rai · 6 months, 3 weeks ago

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eachpair. Notapair. – Siddhartha Srivastava · 6 months, 3 weeks agoLog in to reply

– Ayush Rai · 6 months, 3 weeks ago

that makes no difference.Log in to reply

here or this. Notice how none of them refer to only two elements when talking about pairwise distinct elements. – Siddhartha Srivastava · 6 months, 3 weeks ago

You can check the top commentLog in to reply

– Ayush Rai · 6 months, 3 weeks ago

I still don't agree with you.Log in to reply

– Siddhartha Srivastava · 6 months, 3 weeks ago

Sure. No problem.Log in to reply

– Ayush Rai · 6 months, 3 weeks ago

Did you ask the staff about this question??Log in to reply

– Ayush Rai · 6 months, 3 weeks ago

ok, ask calvin lin about this.Log in to reply

– Ayush Rai · 6 months, 3 weeks ago

you are absolutely correct.Did you appear for the NMTC 2nd level test?Log in to reply

– Svatejas Shivakumar · 6 months, 3 weeks ago

nope. I came to know about this exam this year only. Have you written it?Log in to reply

– Ayush Rai · 6 months, 3 weeks ago

Can solve the other set of problems?their also from NMTC.Log in to reply

– Ayush Rai · 6 months, 3 weeks ago

Yes! It was really tough for me.Log in to reply