PrimeQCertificate | Example Notebook

A certificate that can be used to prove that

1093

is a prime:

In[6]:=

[◼]	PrimeQCertificate

[1093]

Out[6]=

{1093,5,{2,{3,2,{2}},{7,3,{2,{3,2,{2}}}},{13,2,{2,{3,2,{2}}}}}}

The same certificate can be obtained by using

with the option

"Certificate"->

True

:

In[21]:=

ResourceFunction["ProvablePrimeQ"][1093,"Certificate"->True]

Out[21]=

{True,{1093,5,{2,{3,2,{2}},{7,3,{2,{3,2,{2}}}},{13,2,{2,{3,2,{2}}}}}}}

———

A certificate that can be used to prove that

1093×3511

is composite:

In[1]:=

[◼]	PrimeQCertificate

[10933511]

Out[1]=

{2,3837522,3837523}

The output is a list of three integers that indicate

1093×3511

is composite, and that it violates Fermat's little theorem for primes,

p-1

2

≡1modp

if

p

is prime:

In[2]:=

PowerMod@@%

Out[2]=

3134697