Well, no surprises here, it's composite:
[CODE]M125731369/"1" interim We8 residue EE9CB5973F87EBC5 at iteration 123000000
M125731369/"1" interim We8 residue ED1BBFF1E242A1AC at iteration 124000000
M125731369/"1" interim We8 residue FF77A5DC9D544CBD at iteration 125000000
[Wed Feb 10 22:50:05 2016]
M125731369/M11213 is not prime. RES64: 7B39D9067F3A3A06. We8: 00000000,00000000[/CODE]

Good to know for sure. Nice work making it possible to test them in a reasonable amount of time.

[QUOTE=Batalov;425395]
EDIT: this patch-2.0 works much better:[/QUOTE]

Attached is the updated ecm.c file. It includes this upgrade and another of your Phi changes.

Sieved M(77232917^2) / M(77232917) without finding a factor and sieved some of the lower ones some more without any new factors..


[CODE]p Factor(s) of M(p^2)/M(p) k in 2*k*p^2+1
----------------------------------------------------------------------------------------
2 [COLOR="Lime"]Prime[/COLOR]
3 [COLOR="Lime"]Prime[/COLOR]
5 601,1801 k=12,36
7 [COLOR="Lime"]Prime[/COLOR]
13 4057 k=12
17 12761663 k=22079
19 9522401530937 k=13188921788
31 280651416271709745866686729 k=146020507945738681512324
61 80730817,301780543,281646330073 k=10848,40551,37845516
89 29123869433,49849688719 k=1838396,3146679
107 1167799,377175857 k=51,16472
127 14806423,25044595073,72653532113 k=459,776384,2252264
521 8143231,10857641,4338170063 k=15,20,7991
607 345899921201,166969148315503 k=469400,226583799
1279 103097448872275370551 k=31512062869275
2203 15714690743 k=1619
2281 [COLOR="DeepSkyBlue"]Composite[/COLOR] (No factor 2*k*p^2+1 < 2^73) (k<90*10^13))
3217 102559471991 k=4955
4253 1844976919,57592220657 k=51,1592
4423 [COLOR="DeepSkyBlue"]Composite[/COLOR] (No factor 2*k*p^2+1 < 2^74) (k<48*10^13))
9689 76729816024661281759 k=408673285599
9941 [COLOR="DeepSkyBlue"]Composite[/COLOR] (No factor 2*k*p^2+1 < 2^76) (k<38*10^13))
11213 [COLOR="DeepSkyBlue"]Composite[/COLOR] (No factor 2*k*p^2+1 < 2^77) (k<60*10^13))
19937 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^78) (k<38*10^13))
21701 33907204873,153745627424471 k=36,163235
23209 17206738756236217 k=15971868
44497 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^81) (k<61*10^13))
86243 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^77.9) (k<2*10^13))
110503 250836575030879,22513968547647823 k=10271,921879
132049 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^79.2) (k<2*10^13))
216091 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^80.6) (k<2*10^13))
756839 696531210655937,63659341689518360417 k=1216,55568048
859433 17727001955737,667717073666057 k=12,452
1257787 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^85.7) (k<2*10^13))
1398269 34207412811532057 k=8748
2976221 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^88.1) (k<2*10^13))
3021377 2329356963700884673 k=127584
6972593 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^90.6) (k<2*10^13))
13466917 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^92.5) (k<2*10^13))
20996011 899298254940726841 k=1020
24036583 5274651651287933470393 k=4564764
25964951 20225360412972031 k=15
30402457 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^94.9) (k<2*10^13))
32582657 3322246487577398706217 k=1564692
37156667 71776963464264825905447 k=25994507
42643801 901972906808890097 k=248
43112609 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^95.9) (k<2*10^13))
57885161 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^96.7) (k<2*10^13))
74207281 508014103943653104553301983 k=46126737231
77232917 [COLOR="Red"]Unknown[/COLOR] (No factor 2*k*p^2+1 < 2^97.6) (k<2*10^13))
[/CODE]

the small ones (13, 17, 19) can be easily full factored (19^2-19=384-19 bits, about 100 digits)
[CODE]
gp > factorint(m2(p))
time = 647 ms.
[ 4057 1]
[ 6740339310641 1]
[3340762283952395329506327023033 1][/CODE]

[QUOTE=Jens K Andersen;242124]Getting back to the pointless computations instead of discussing their pointlessness, at [url]http://donovanjohnson.com/mersenne.html[/url] I think I found the 5 largest known probable Mersenne semiprimes :
M(684127) = 23765203727 * prp205933
M(406583) = 813167 * prp122388
M(271549) = 238749682487 * prp81734
M(271211) = 613961495159 * prp81631
M(221509) = 292391881 * prp66673

The largest proven Mersenne semiprime at [url]http://primes.utm.edu/top20/page.php?id=49[/url] is:
M(17029) = 418879343 * p5118[/QUOTE]

Updating the above post from 2010, which is about the boring kind:

The original list above is missing the entries:

M(611999) = 18464214225958267477777390354183 * prp184199
M(432457) = 1672739247834685086279697 * prp130159

Of course, every unfactored Mersenne number of prime exponent is potentially a semiprime, so more entries may be added at any time as new factors are found.


The largest known probable Mersenne semiprimes are:

M(7313983) = 305492080276193 * prp2201714
M(5240707) = 75392810903 * prp1577600
M(4187251) = 72234342371519 * prp1260475
M(3464473) = 604874508299177 * prp1042896
M(2327417) = 23915387348002001 * prp700606

The largest proven Mersenne semiprime is:

M(63703) = 42808417 * p19169

and the next semi-feasible candidate for Primo certification is:

M(86371) = 41681512921035887 * prp25984

[QUOTE=GP2;482974]Updating the above post from 2010, which is about the boring kind:

The original list above is missing the entries:

M(611999) = 18464214225958267477777390354183 * prp184199
M(432457) = 1672739247834685086279697 * prp130159

[/QUOTE]
These do not appear in that list because they were found after 2010. There are lots of Mersenne semiprimes, but the problem is to find the smallest prime factor.

PS. Maybe in the future someone will find an algorithm to quickly detect probable semiprimes. In [url]http://physics.open.ac.uk/~dbroadhu/cert/semgpch.gp[/url] you can find a 5061-digit proven semiprime, but the certificate does not need the prime factors.