MHB Largest Even Integer: Impossible Sum of Two Odd Composites

  • Thread starter Thread starter anemone
  • Start date Start date
  • Tags Tags
    even Integer
AI Thread Summary
The discussion centers on identifying the largest even integer that cannot be expressed as the sum of two odd composite numbers. Participants express confusion regarding the concept of bounding such an integer, especially considering the infinite nature of odd primes. The challenge lies in the properties of odd composites and their sums, which may not cover all even integers. The conversation highlights the complexities involved in number theory related to composite numbers. Ultimately, the quest remains to determine this elusive largest even integer.
anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
Find the largest even integer which cannot be written as the sum of two odd composite numbers.
 
Mathematics news on Phys.org
anemone said:
Find the largest even integer which cannot be written as the sum of two odd composite numbers.
I must be missing something. Say we have a, b, c, d are all odd primes. Then e = ab + cd. But there is no largest prime so how can e be bounded?

-Dan
 
anemone said:
Find the largest even integer which cannot be written as the sum of two odd composite numbers.
I will use the notation $*5$ to denote any positive integer ending in $5$, apart from the number $5$ itself. So $*5$ could be $15,25,35,\ldots$. Notice that any number of the form $*5$ is odd and composite.

The smallest odd composite numbers are $9,15,21,25,27,33,\ldots$.

If an even integer ends in $0$ and is greater than $20$ then it is of the form $15 + *5$.

If an even integer ends in $2$ and is greater than $32$ then it is of the form $27 + *5$.

If an even integer ends in $4$ and is greater than $14$ then it is of the form $9 + *5$.

If an even integer ends in $6$ and is greater than $26$ then it is of the form $21 + *5$.

If an even integer ends in $8$ and is greater than $38$ then it is of the form $33 + *5$.

The largest even number not included in any of those categories is $38$. You can easily verify that $38$ cannot be expressed as the sum of two odd composite numbers. So it is the largest such even number.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top