Win a copy of Spring in Action (5th edition) this week in the Spring forum!
  • Post Reply Bookmark Topic Watch Topic
  • New Topic
programming forums Java Mobile Certification Databases Caching Books Engineering Micro Controllers OS Languages Paradigms IDEs Build Tools Frameworks Application Servers Open Source This Site Careers Other all forums
this forum made possible by our volunteer staff, including ...
Marshals:
  • Campbell Ritchie
  • Bear Bibeault
  • Devaka Cooray
  • Liutauras Vilda
  • Jeanne Boyarsky
Sheriffs:
  • Knute Snortum
  • Junilu Lacar
  • paul wheaton
Saloon Keepers:
  • Ganesh Patekar
  • Frits Walraven
  • Tim Moores
  • Ron McLeod
  • Carey Brown
Bartenders:
  • Stephan van Hulst
  • salvin francis
  • Tim Holloway

Highest Number of Consecutive Primes  RSS feed

 
Ranch Hand
Posts: 89
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator

Euler published the remarkable quadratic formula:

n� + n + 41

It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41� + 41 + 41 is clearly divisible by 41.

Using computers, the incredible formula n� − 79n + 1601 was discovered, which produces 80 primes for the consecutive values n = 0 to 79. The product of the coefficients, −79 and 1601, is −126479.

Considering quadratics of the form:

n� + an + b, where |a| < 1000 and |b| < 1000

where |n| is the modulus/absolute value of n
e.g. |11| = 11 and |−4| = 4

Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.



This is weird, the code I wrote is very simple, it gives correct answers for a = 1 b = 41 and a=-79 b = 1601
but when I run it to find the largest number of consecutive primes, I get 1011 consecutive prime numbers when a = -999 and b = 61
making the product -60939
but this is turning out to be the wrong answer...
anyone can find me an error in the code?
 
Wanderer
Posts: 18671
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
Well, look at the "prime" numbers generated by the formula when a = -999 and b = 61. What do you get when n = 0? n = 1? n = 2? Are all those numbers prime? If not, how can you modify the isPrime() method to correctly identify whether a number is prime or not?
 
Consider Paul's rocket mass heater.
  • Post Reply Bookmark Topic Watch Topic
  • New Topic
Boost this thread!