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#41 by Joerg Arndt at Fri Mar 08 11:57:50 EST 2024
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#40 by Paolo P. Lava at Fri Mar 08 06:43:05 EST 2024
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Primes of the form F(k+5)-F(k), where F(k) is a Fibonacci number. - Paolo P. Lava, Jul 19 2012
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approved
editing
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#39 by Sean A. Irvine at Sat Mar 18 16:43:54 EDT 2023
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#38 by Alois P. Heinz at Mon Feb 27 08:20:40 EST 2023
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#37 by Alois P. Heinz at Mon Feb 27 08:18:10 EST 2023
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7, 19, 31, 131, 1453, 2351, 42187, 1981891, 3206767, 13584083, 332484016063, 66165989928299, 146028309791690867, 1619478772188347101, 47020662244482792763, 229030451631542624193448579, 1569798068858809572115420691
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proposed
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#36 by Michel Marcus at Mon Feb 27 03:57:00 EST 2023
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Discussion
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| Mon Feb 27
| 07:12
| Rigoberto Florez: @Schoenfield. That is correct. The correct statement is as you wrote.
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#35 by Michel Marcus at Mon Feb 27 03:56:56 EST 2023
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Are there infinitely many primes of the form F(k+3)+L(k+2)? There are 47 primes of this form for k <= 80,00080000. There are no such primes for 64,00064000 <= k <= 80,00080000. - Rigoberto Florez, Feb 26 2023
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#34 by Joerg Arndt at Mon Feb 27 03:54:49 EST 2023
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#33 by Joerg Arndt at Mon Feb 27 03:54:17 EST 2023
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Are there infinitely many primes of the form F(k+3)+L(k+2)? Searching for thisThere typeare of47 primes the computer algebra package Mathematicaof showedthis thatform for k= <= 80,000, there are 47 primes of this form. The computer did notThere findare anyno newsuch primeprimes for k between 64,000 and <= k <= 80,000. - Rigoberto Florez, Feb 26 2023
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proposed
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#32 by Rigoberto Florez at Sun Feb 26 15:26:02 EST 2023
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Discussion
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| Sun Feb 26
| 19:38
| Jon E. Schoenfield: "Are there infinitely many primes of the form F(k+3)+L(k+2)? Searching for this type of primes the computer algebra package Mathematica showed that for k=80,000, there are 47 primes of this form." I don't understand. For k=80000, there's just one number of the form F(k+3)+L(k+2): it's F(80003)+L(80002).
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| 21:49
| Rigoberto Florez: @Schoenfield. I put your number in Mathematica: PrimeQ[Fibonacci[80003] + LucasL[80002]] the answer was False. However, if I am wrong and you can show that this number is prime it will be a great news. It gives more evidences for the question. Can you ask to your computer if it can factor Fibonacci[80003] + LucasL[80002]. Maybe you have a better computer than I do. I am going to do the same as soon as I get my office tomorrow. That is a better computer.
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| 23:41
| Jon E. Schoenfield: I'm sorry that what I wrote was unclear. I should have written, "For k=80000, there's just one number of the form F(k+3)+L(k+2): it's F(80003)+L(80002), and it is not a prime."
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| 23:43
| Jon E. Schoenfield: When you wrote "for k=80,000, there are 47 primes of this form", I'm guessing you meant "for k <= 80,000, there are 47 primes of this form." Is this correct?
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