Graduate Unsolved problems in number theory and news about them

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The discussion centers on several prominent unsolved problems in number theory, specifically the Riemann hypothesis, Goldbach conjecture, twin primes conjecture, and the infinitude of prime numbers. Participants are encouraged to share any updates or proofs related to these conjectures. The thread highlights the ongoing interest in these mathematical challenges and invites further discussion on their implications. The original poster expresses gratitude for the opportunity to engage with the community. The thread concludes with a note that it will be closed.
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Hello people of physicsforums. Has anyone proved these problems in number theory :Riemann hypothesis, Goldbach conjecture, twin primes conjecture, infinitude of prime numbers? If you want make discussion about them.

Thank you for allowing me participate in physicsforums and for wanting to make discussions on topics of math, physics and other sciences. Have a good day.
 
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I’m closing this thread now.

These unsolved problems are easy to look up via google.
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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