Browse Groups

• ## 35 successive primes not full period

(12)
• NextPrevious
• ... 10 is not a primitive root of unity modulo any of the 35 consecutive primes beginning with 1292613521 n=35;p=1292613521;v=vector(n);
Message 1 of 12 , Aug 8, 2009
View Source

> Any advance on 33 consecutive primes of this kind?

10 is not a primitive root of unity modulo any of
the 35 consecutive primes beginning with 1292613521

n=35;p=1292613521;v=vector(n);
for(k=1,n,v[k]=(p-1)/znorder(Mod(10,p));p=nextprime(p+1));
print(v);

[10, 2, 2, 2, 2, 3, 2, 7, 2, 2, 4, 3, 4, 2, 3, 8, 14, 4,
2, 6, 2, 6, 2, 2, 3, 12, 2, 2, 3, 21, 2, 2, 3, 3, 10]

David
• ... Ah, Jens beat my case with 35, which was to be expected. David
Message 1 of 12 , Aug 8, 2009
View Source
"Jens Kruse Andersen" <jens.k.a@...> wrote:

> > Any advance on 33 consecutive primes of this kind?
>
> [35, 1292613521, 1292614321]
> [36, 2757553987, 2757554983]

Ah, Jens beat my case with 35, which was to be expected.

David
• ... [37, 7088772637, 7088772653] David
Message 1 of 12 , Aug 8, 2009
View Source
"Jens Kruse Andersen" <jens.k.a@> wrote:

> [36, 2757553987, 2757554983]

[37, 7088772637, 7088772653]

David
• ... Whoops! The last of these 37 primes is 7088773519 n=37;p1=7088772637;v=vector(n);p=p1; for(k=1,n,v[k]=(p-1)/znorder(Mod(10,p));p2=p;p=nextprime(p+1));
Message 1 of 12 , Aug 8, 2009
View Source

> [37, 7088772637, 7088772653]

Whoops! The last of these 37 primes is 7088773519

n=37;p1=7088772637;v=vector(n);p=p1;
for(k=1,n,v[k]=(p-1)/znorder(Mod(10,p));p2=p;p=nextprime(p+1));
print([n,p1,p2,v]);

[37, 7088772637, 7088773519,
[2, 52, 2, 2, 2, 10, 4, 6, 2, 4, 2, 2, 2, 6, 2, 2, 8, 4,
3, 2, 2, 3, 3, 60, 3, 2, 4, 35, 3, 4, 4, 3, 2, 25, 2, 2, 2]]

With apologies for the typo,

David
• ... 10 is not a primitive root of unity modulo any of the 40 consecutive primes beginning with 22588287443 n=40;p1=22588287443; v=vector(n);p=p1;
Message 1 of 12 , Aug 8, 2009
View Source

> 37, 7088772637, 7088773519

10 is not a primitive root of unity modulo any of
the 40 consecutive primes beginning with 22588287443

n=40;p1=22588287443;
v=vector(n);p=p1;
for(k=1,n,v[k]=(p-1)/znorder(Mod(10,p));p2=p;p=nextprime(p+1));
print([n,p1,p2,v]);

[40, 22588287443, 22588288409,
[46, 15, 5, 2, 2, 5, 2, 2, 2, 2, 7, 2, 5, 9, 7, 30, 2, 4, 3, 3,
3, 4, 3, 3, 2, 6, 2, 9, 2, 16, 2, 2, 2, 2, 2, 6, 48, 5, 2, 2]]

David
• ... 10 is not a primitive root of unity modulo any of the 45 consecutive primes beginning with 24124140487 n=45;p1=24124140487; v=vector(n);p=p1;
Message 1 of 12 , Aug 8, 2009
View Source

> 10 is not a primitive root of unity modulo any of
> the 40 consecutive primes beginning with 22588287443

10 is not a primitive root of unity modulo any of
the 45 consecutive primes beginning with 24124140487

n=45;p1=24124140487;
v=vector(n);p=p1;
for(k=1,n,v[k]=(p-1)/znorder(Mod(10,p));p2=p;p=nextprime(p+1));
print([n,p1,p2,v]);

[45, 24124140487, 24124141903,
[3, 2, 6, 2, 2, 90, 6, 3, 7, 4, 8, 3, 12, 4, 4,
2, 2, 9, 20, 6, 7, 2, 4, 2, 36, 42, 2, 2, 2, 2,
2, 2, 117, 10, 3, 15, 3, 4, 2, 2, 10, 2, 2, 2, 7]]

David
Your message has been successfully submitted and would be delivered to recipients shortly.
• Changes have not been saved
Press OK to abandon changes or Cancel to continue editing
• Your browser is not supported
Kindly note that Groups does not support 7.0 or earlier versions of Internet Explorer. We recommend upgrading to the latest Internet Explorer, Google Chrome, or Firefox. If you are using IE 9 or later, make sure you turn off Compatibility View.