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 April 11th, 2017, 03:50 AM #1 Newbie   Joined: Apr 2017 From: poland Posts: 1 Thanks: 0 Pythagorean prime in every prime twin Hi, I have a thread to understand, but I have some problem with it. I must prove that in every prime twin there is one and only one Pythagorean prime. I found something about it on 5 page of: www.fq.math.ca/Scanned/24-2/sternheimer.pdf Can anyone explain it a bit easier? Thank you a lot. Last edited by skipjack; April 12th, 2017 at 05:44 AM. April 12th, 2017, 03:21 AM #2 Math Team   Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234 A Pythagorean Prime is of the form $4n + 1$ so the best you can do is to have $2$ consecutive Pythagorean Primes differ by $4$ , like $13$ and $17$ Twin primes differ by $2$ exactly so it is impossible to have $2$ Pythagorean Primes in any set of twin primes $(p_1 , p_2)$ Last edited by agentredlum; April 12th, 2017 at 03:39 AM. Reason: fixed error April 12th, 2017, 03:35 AM #3 Math Team   Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234 Any prime greater than $2$ must be of the form $4n + 1$ or $4n- 1$ Consider the arbitrary twin prime ordered pair $(p_1, p_2)$ with $p_1 < p_2$ and $2$ cases Case 1 If $p_1$ is of the form $4n + 1$ then $p_2$ must be of the form $4n + 3$ so only $1$ Pythagorean Prime in this case Case 2 If $p_1$ is of the form $4n- 1$ then $p_2$ is of the form $4n + 1$ so only $1$ Pythagorean Prime in this case This exhausts all possible cases for twin primes given your conditions  Tags prime, pythagorean, twin Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post billymac00 Number Theory 38 December 21st, 2013 09:29 AM chibeardan New Users 7 May 26th, 2013 07:39 PM Macky Number Theory 8 September 28th, 2010 12:39 PM ogajajames Number Theory 4 April 26th, 2010 06:51 AM momo Number Theory 19 April 11th, 2010 10:54 AM

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