OFFSET
1,1
COMMENTS
There are primes like p = 20393, 3905513, 5177033, 28398833, or 10877895569 which have more than one representation p=x^4-y^3, with x,y>=1.
My guess is that the number of duplicates is infinite.
FORMULA
If x^4-y^3 is prime for integers x >=1, y>=1, list it.
PROG
(PARI) difffourthcube(n) =
{
local(a, c=0, c2=0, j, k, y);
a=vector(floor(n^2/log(n^2)));
for(j=1, n,
for(k=1, n,
y=j^4-k^3;
if(ispseudoprime(y),
c++;
\\ print(j", "k", "y);
a[c]=y;
);
);
);
a=vecsort(a);
for(j=2, c,
if(a[j]!=a[j-1]&&a[j]!=0,
c2++;
print1(a[j]", ");
if(c2>100, break);
);
);
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Jun 17 2009
STATUS
approved