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The RSA factoring challenge lists this RSA 2048 value:

25195908475657893494027183240048398571429282126204032027777137836043662020707595556
26401852588078440691829064124951508218929855914917618450280848912007284499268739280728777
67359714183472702618963750149718246911650776133798590957000973304597488084284017974291006
42458691817195118746121515172654632282216869987549182422433637259085141865462043576798423
38718477444792073993423658482382428119816381501067481045166037730605620161967625613384414
36038339044149526344321901146575444541784240209246165157233507787077498171257724679629263
86356373289912154831438167899885040445364023527381951378636564391212010397122822120720357

Is this number used for factoring challenge only? Lets say one day a VERY VERY lucky guy just GUESS the factor P and Q correctly will there be any security issue in the world. Is anyone using this particular RSA 2048 for anything?

My initial thought was that this number was extremely important but I guess it is just one of the many RSA 2048 out there. Cracking this one by luck doesn't mean much right?

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  • $\begingroup$ That kind of luck doesn't exist. $\endgroup$ – Maarten Bodewes Nov 2 at 12:28
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Is this number used for factoring challenge only? Lets say one day a VERY VERY lucky guy just GUESS the factor P and Q correctly will there be any security issue in the world. Is anyone using this particular RSA 2048 for anything?

I don't believe so. On occasion, the need for a composite of unknown (to anybody) factorization comes up; someone might be using it for that. Such numbers are harder to generate than you might think; if you just select a random 2048 value, find that it is composite, and run ECM on it a bunch, well, you won't know whether running ECM a bit longer would find the factorization. Using one of the RSA challenge numbers would make sense in that case, but again, I don't know of anyone who's actually doing it.

On the other hand,

Cracking this one by luck doesnt mean much right?

While there isn't a great deal of significance to this specific number, if someone did manage to factor it, it would certain raise the issue whether other 2048 bit numbers were hard to factor (which, incidentally, is precisely why RSA generated their challenge numbers in the first place)

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