- L2738 (2,74) 70531186979083.P543

settles the matter, in my mind.

I cannot believe that Blair Kelly

missed a p18*p544 split at a smaller index.

Please see:

http://home.att.net/~blair.kelly/mathematics/fibonacci/status3000.html

And you have *no* composite to appeal to

larger than these

L2687 C562

L2692 (4) C562

L2731 3371665291.C562

as far as I can tell.

David - "David Broadhurst" wrote:
> L2738 (2,74) 70531186979083.P543>

Then I agree, any of these composites, would not have a prime larger

> settles the matter, in my mind.

> I cannot believe that Blair Kelly>

> missed a p18*p544 split at a smaller index.

>

> L2687 C562

> L2692 (4) C562

> L2731 3371665291.C562

than p543.

Hats off to David!

I will be silent now, while I try and redeem myself.

Shane F. - Shane:

> Then I agree, any of these composites,

Yes, but that *idiot* Broadhurst overlooked the fact

> would not have a prime larger than p543.

2738=2^2*37^2

and you had cunningly included this type of

"limited cyclotomic disadvantage"

when the two odd primes are not distinct!

So you can survive the p19 squeeze from

p543|L(2^2*37^2)

because of your get-out clause "p^m" in the title.

However there are at least three

"severely cyclotomically disadvantaged"

aspiring largest-yet record holders:

p609|L(2*29*53)

p913|L(2*43*53)

p1793|L(67*131)

needing some ECM work to rule out

already highly implausible splits

of a few nearby composites with no

more than 31 extra digits

P.C. warning : Anyone found to be running extra ECM on

a few carefully selected composites 30 digits larger

than one of these putative paraplegic record holders,

in the *very* remote hope of extracting a W.A.S.P.

prime that might displace it, will be reported to

the suitable authorities for politically incorrect

persecution of a severely disadvantaged minority :-) - Shane:

> q | L(0)

If you omit the requirement that the index

> q=2

be a natural number, then a much funnier

thing than that happens:

2|L(0) is not a record because 3|L(-2)

? L(n)=if(n,fibonacci(2*n)/fibonacci(n),2);

? if(L(-2)%3==0,print(ok))

ok

3|L(-2) is not a record because 7|L(-4):

? if(L(-4)%7==0,print(ok))

ok

and so on, showing that *no* record exists :-)

> lol

loss of logic?

David