You are here:

Number Theory/number theory, primes

Advertisement


Question
Informally:
 Take any positive whole number.  Can you create a prime number by adding digits to the end of the number?

Formally: Let N be the positive whole number written d1d2d3...dm.
di being 0 to 9, d1 not equal to 0.  Is there a prime number that has d1d2d3...dm for its first m digits?

Not use to writing math on a keyboard.
Has this question ever been investigated?  Is it trivial?

Thank you in advance for your time , knowledge and effort.

Answer
Hello Emil
I've never seen this before.  But I'm pretty sure there are an infinity of prime numbers that start with those m digits.  There must be a short proof, but I can't think of one immediately.  
I'll get back to you if I come up with one.
best wishes
vijilant

Number Theory

All Answers


Answers by Expert:


Ask Experts

Volunteer


Vijilant

Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

Experience

Teacher of math for 53 years

Organizations
AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

Publications
Journal of mathematics and its applications M500 magazine

Education/Credentials
BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors
State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 50 prize First class honours in OU BA Mathematics

Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.

©2016 About.com. All rights reserved.