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K Sengupta
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Ten distinct prime numbers, each less than 3000, when arranged in increasing order of magnitude describe an arithmetic sequence.
What are these ten prime numbers?
What are these ten prime numbers?
Jarle said:But the sum of the prime numbers p and p+d are even, but also equal to the prime number p+3d, a contradiction.
jimmysnyder said:Here's an easy question. This is a run of length 10. There are two runs of length 9. What are they?
Jarle said:They are on the form p,p+d,p+2d..., where p is an odd prime and d is a positive integer. But the sum of the prime numbers p and p+d are even, but also equal to the prime number p+3d, a contradiction.
This isn't jeopardy. Pose your answer in the form of an answer.davee123 said:Are you implying that there are more runs of 9 besides the 2 included within your run of 10?
jimmysnyder said:This isn't jeopardy. Pose your answer in the form of an answer.
An arithmetic sequence is a series of numbers in which the difference between any two consecutive terms is constant. For example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence with a common difference of 3.
Prime numbers are numbers that are only divisible by 1 and themselves. They cannot be divided evenly by any other numbers.
To find ten prime numbers in an arithmetic sequence, you can start with any prime number and add the common difference repeatedly until you have ten prime numbers. For example, if you start with the prime number 5 and a common difference of 3, you would get the sequence 5, 8, 11, 14, 17, 20, 23, 26, 29, 32.
Ten prime numbers in an arithmetic sequence can be useful in mathematical patterns and equations. They can also provide insights into the distribution and relationships of prime numbers.
Yes, ten prime numbers in an arithmetic sequence can be found in real-world applications such as cryptography, where prime numbers are used in creating secure codes and algorithms. They can also be found in nature, such as the pattern of leaf arrangement on a stem or the spiral arrangement of seeds in a sunflower.