Primorial puzzle

 
 
                                                                   Part 1

 
 

To find   (m, n)   so that   C(m,n)   is a product of all prime numbers ≤ m

For example,

 
PRIMORIAL 1

 
 
 
 
 
 

                                                                   Part 2

 
 

To find   (m, n)   so that   C(m,n)   is a product of consecutive prime numbers

 
Paul found:

 
PRIMORIAL 2

and

PRIMORIAL 3

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Posted in Number Puzzles | Tagged | 2 Comments

when the sum of consecutive cubes is a square

 

Nicomachus’s Theorem
http://mathworld.wolfram.com/NicomachussTheorem.html

 
SUMS 2

 
 

To find a sum of four or more consecutive cubes – not starting with 1 – giving us the square of an integer

 
 

Paul found:

 
SUMS 1

 
 
From Republic of Math :

 
SUMS 3

 

From Derek :

 
SUMS 4

 
 
 
 
 
 
 
 
 
 
 
 
 
 

Posted in Uncategorized | Tagged , | 2 Comments

Integers (A,B); A+B, A^2 + B^2 and A^3 + B^3 are all squares

 

RARE 1

 
 
David found:

 
RARE 2

 
 
 
 
 
 
 

Posted in Number Puzzles | Tagged , | 1 Comment

Equation | a^7 + b^3 = c^2, gcd(a,b,c) = 1

 
 
a7 + b3 = c2

 
David Radcliffe sent me a link to “primitive solutions to x^2 + y^3 = z^7″

http://arxiv.org/abs/math/0508174v1

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Posted in Number Puzzles | Tagged , | Leave a comment

Difference of two consecutive cubes

 
 

Difference of 2 CUBES 1

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Posted in Number Puzzles | Tagged | Leave a comment

Grid | Numbers from 1 to 25

 
 
Find the arrangement of the array :

 
5by5 multiplicative grid 1

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Posted in Number Puzzles | Tagged , | 3 Comments

Puzzle | Primes with prime subscripts

 

Primes with prime subscripts
A006450

3,   5,   11,   17,   31,   41,   59,   67,   83,   109,   127,   157,   179,   191,   211,   241,   277,   283,   331,   353,   367,   401,   431,   461,   509,   547,   563,   587,   599,   617,   709,   739,   773,   797,   859,   877,   919,   967,   991,   1031,   1063,   1087,   1153,   1171,   1201,   1217,   1297,   1409,   1433,   1447,   1471,   …

 
SUPERPRIMES 4
 
 

Derek found:

(158161, 158227, 158293, 158359)
(371131, 371941, 372751, 373561)

 

SUPERPRIMES 5

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

Posted in Number Puzzles | Tagged , | 7 Comments