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cwrw238

  • 3 years ago

Solve in prime numbers pq + p + q + 2 = p^2.

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  1. cwrw238
    • 3 years ago
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    Similar to mukushla's previous post.

  2. cwrw238
    • 3 years ago
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    both p and q are prime

  3. eliassaab
    • 3 years ago
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    You can I think show that p-q =2

  4. eliassaab
    • 3 years ago
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    Here is a sequence for up to 100th prime of (p,q) {{5, 3}, {7, 5}, {13, 11}, {19, 17}, {31, 29}, {43, 41}, {61, 59}, {73, 71}, {103, 101}, {109, 107}, {139, 137}, {151, 149}, {181, 179}, {193, 191}, {199, 197}, {229, 227}, {241, 239}, {271, 269}, {283, 281}, {313, 311}, {349, 347}, {421, 419}, {433, 431}, {463, 461}, {523, 521}}

  5. mukushla
    • 3 years ago
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    \[pq + p + q + 2 = p^2\]\[q=\frac{p^2-p-2}{p+1}=\frac{p^2+p-2p-2}{p+1}=p-2\]

  6. Herp_Derp
    • 3 years ago
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    \[pq+p+q+2=p^2\]\[p(q+1)+q+2=p^2\]\[(p+1)(q+1)+1=(p+1)(p-1)+1\]\[q+2=p\]\(p\) and \(q\) are twin primes... But it's an open conjecture on whether there are an infinite number of twin primes... http://mathworld.wolfram.com/TwinPrimeConjecture.html

  7. mukushla
    • 3 years ago
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    i was lookin for it ... thank u herp derp...its open

  8. Herp_Derp
    • 3 years ago
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    Impossible to solve!!!?!

  9. mukushla
    • 3 years ago
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    Open Questions of primes http://primes.utm.edu/notes/conjectures/ i have a nice article about open questions...i cant find it now..i'll upload it later.

  10. cwrw238
    • 3 years ago
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    thanks guys

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