Mersenne Semiprimes

[NBtarheel_33]

Originally Posted by R.D. Silverman

You might want to consider the reason why noone else had done it before...

I thought "no one" was always two words...

[cmd]

Originally Posted by NBtarheel_33

I thought "no one" was always two words...

why

all attacked, you write "separate"
separate, you write "all attacked"

[CRGreathouse]

Originally Posted by NBtarheel_33

I thought "no one" was always two words...

Linguistically, it's one word. It's not surprising to me that conventions increasingly support this spelling (though it's still nonstandard at the moment).

[davar55]

A certain person in this forum posted the following line earlier
in this thread:

You might want to consider the reason why no one else had done it before...

in response to another posters explanation of his motivations.

We are GIMPS supporters, not RDSers.

P95 is a great program, but math rules.

[cmd]

Always be skeptical to any news

[davar55]

For more info on why semi-primes are relevant to our search
for Mersennes, see the thread Mersenne-Like in the Puzzles subforum.

Link is: Mersenne-Like

The list there could be extended.

[ATH]

I trialfactored the last 15 exponent with no factors a bit further but with no luck. I'm stopping for now:

p		Factor(s) of M(p2)/M(p)
--------------------------------------------------
2281		No factor 2*k*p2+1 < 271 (k<226*1012)
4423		No factor 2*k*p2+1 < 273 (k<241*1012)
9941		No factor 2*k*p2+1 < 275 (k<191*1012)
11213		No factor 2*k*p2+1 < 276 (k<300*1012)
19937		No factor 2*k*p2+1 < 277 (k<190*1012)
44497		No factor 2*k*p2+1 < 280 (k<305*1012)
86243 		No factor 2*k*p2+1 < 273.7 (k<1.1*1012)
132049 		No factor 2*k*p2+1 < 275.0 (k<1.1*1012)
216091 		No factor 2*k*p2+1 < 276.4 (k<1.1*1012)
1257787 	No factor 2*k*p2+1 < 281.5 (k<1.1*1012)
2976221 	No factor 2*k*p2+1 < 284.0 (k<1.1*1012)
6972593 	No factor 2*k*p2+1 < 286.4 (k<1.1*1012)
13466917	No factor 2*k*p2+1 < 288.3 (k<1.1*1012)
30402457	No factor 2*k*p2+1 < 290.7 (k<1.1*1012)
43112609	No factor 2*k*p2+1 < 291.7 (k<1.1*1012)

[Mr. P-1]

Thanks for your efforts.

[Brian-E]

axn's recent discovery from another thread:

Originally Posted by axn

There is something to be said for dumb luck.

M3464473/604874508299177 is a probable prime! We4: E866B6FC,00000000

Still need to do some (slow) independent check with PFGW. Ugh!

EDIT:- Anybody know how to make P95 use a different base to do the PRP test?

Originally Posted by alpertron

That's the first Mega-PRP cofactor of a Mersenne number known. Congratulations.

Presumably this makes M3464473 the largest known "probable Mersenne semiprime" too, if that is the correct expression?

On a general point, can anyone say what is currently conjectured about the frequency of occurrence of Mersenne semiprimes? Would we expect them to occur with similar order of frequency to that of Mersenne primes? I note RDS' statement in post #2 of this thread that Mersenne semiprimes with exponent the square of the exponent of a Mersenne Prime would be expected to be finite in number, but what about those Mersenne semiprimes with prime exponent?

[R.D. Silverman]

Originally Posted by Brian-E

On a general point, can anyone say what is currently conjectured about the frequency of occurrence of Mersenne semiprimes? Would we expect them to occur with similar order of frequency to that of Mersenne primes?

No. A full explanation may be found in Hardy & Wright. We expect them
to occur with the same frequency (up to a small constant necessitated by the form of the numbers) as all other integers with exactly two prime factors.

but what about those Mersenne semiprimes with prime exponent?

What about them? See Hardy & Wright. Do you expect numbers with exactly two prime factors to be fewer than primes?

[alpertron]

Originally Posted by Brian-E

Presumably this makes M3464473 the largest known "probable Mersenne semiprime" too, if that is the correct expression?

You can find at http://www.mersenne.ca/prp.php the current list of "probably completely factored Mersenne numbers".