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 Citrix 2017-09-27 01:28

Super Cullen & Woodall primes

Super Cullen and Woodall defined as:-

C(n)= n*2^(n*n)+1
W(n)= n*2^(n*n)-1

Primes so far
1*2^1-1
1*2^1+1
2*2^4-1
5*2^25+1
9*2^81+1

I think there are finite number of these primes, but I still wanted to search further.
I have checked these up to 5 Million bits and plan to search further.

I am using srsieve to sieve these numbers. Is there a faster sieve software or can gcwsieve be made faster for these numbers?

 Citrix 2017-10-26 09:12

I have completed this to 8M bits. Continuing.

I am using the following code to sieve. Does anyone have any suggestions on how to make this faster? Thanks.

[code]

void SuperCullenWoodallSieve::DoWork64Bit(uint64_t thePrime)
{
uint32_t nmin, nmax;
nmin = 100;
nmax = 32768;

uint64_t temp, power;

temp = thePrime + 1;
temp >> 1;
temp = expmod62(temp, nmax*nmax, thePrime);
power = expmod62(2, 2 * nmax, thePrime);

for (int x = nmax; x >= nmin; x--)
{
if (temp == x)
LogFactor('-', x, 2, thePrime);

if (temp == thePrime - x)
LogFactor('+', x, 2, thePrime);

temp = mulmod62(temp, power, thePrime);
if (temp&1)
{
temp = temp + thePrime;
}
temp >> 1;
if (power&1)
{
power = power + thePrime;
}
power >> 1;
if (power&1)
{
power = power + thePrime;
}
power >> 1;
}
}

[/code]

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