Condition on composite numbers easily factored
Choose two large distinct prime numbers p and q
p = prime q = prime Compute c=pq such that: c=3 Mod 4 and (c +1)/4) = 1 Mod (p1) there exist a Quick way of finding p and q from c Can someone please propose a number ( c ) 
[QUOTE=baih;526821]Choose two large distinct prime numbers p and q
p = prime q = prime Compute c=pq such that: c=3 Mod 4 and (c +1)/4) = 1 Mod (p1) there exist a Quick way of finding p and q from c Can someone please propose a number ( c )[/QUOTE] Purpose??? Examples are easy to find. Infinitely many, in fact. Let c = 3q, q = 1 mod 8. Try e.g. c = 51 
purpose a large number c more than 1024BIT
with p and q also very large p and q ([B]private[/B] [B]key)[/B] c is public i can find pq from c 
[QUOTE=baih;526821]...and
(c +1)/4 = 1 Mod (p1) [/QUOTE] This has no generality. This means that q = 3 Mod (p1). Which is a very poor choice of q tightly tied to p. Even if you can solve it, it is of no practical interest. In ciphers, p and q will never be chosen like that. 
yes i know
but step by step:wink: 
[QUOTE=Batalov;526843]This has no generality.
This means that q = 3 Mod (p1). Which is a very poor choice of q tightly tied to p. Even if you can solve it, it is of no practical interest. In ciphers, p and q will never be chosen like that.[/QUOTE] Maybe the purpose is to be a backdoor for a cryptosystem where p and q are designed to be randomly selected? :ermm: 
[QUOTE=baih;526821]Can someone please propose a number ( c )[/QUOTE]
Sure. Here you go. [CODE]retracting[/CODE] 
:popcorn:
I would have chosen q to be around p^2. I wonder what axn chose. Perhaps we will see. 
[QUOTE=CRGreathouse;526864]:popcorn:
I would have chosen q to be around p^2. I wonder what axn chose. Perhaps we will see.[/QUOTE] q = O(p). Should the need arise, I can do your suggestion. I'm counting on OP being able to factor the number. If not, we may never know the factorization, as I did not record the p, q values. EDIT: q = O(p^2) [code] retracting [/code] 
I had to retract the numbers as they did not properly satisfy OP's requirements.

[CODE]3288315334013507348031117171885468096161021677564004034300356172248483753561621058705350647739894009\
5346045680550009445472595322983664958188142787148092914918061445039917611408596599725591252362294564\ 1600699758076211854269675560352903000577560129603812320249402228524238334224780394198927618762027764\ 4694175629521539892657010544312115079861771453079179141384844469970549673293813989678369426258452910\ 3551493881299669360832439809441334130754552040177986894056672293223072559252965382679545203159671871\ 1052801385883659044607163858197456954994787562252648007765822584016182739358104036624722033623683457\ 3334375676353282746086370455038295247170962866302648507514375876708778979433419266589795636925613207\ 4747459949682410108234198907723945838288102283178012219388623968160789028801889034265955398723460901\ 5349542235839252138730727703428196783513008435899978778140980069771163397970731725281106467346639407\ 481050648890548443151347[/CODE] Try this. q = O(p^2) 
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