I noticed an announcement on the flint-dev list which led me to try
this, and indeed we have the bug:

sage: n=2007193456621
sage: n.is_prime()
False
sage: n.factor()                 # !!!!!!!!!!
2007193456621
sage: pari(n).factor()
[1001797, 1; 2003593, 1]
sage: n == 1001797 * 2003593
True

See flint-dev for more details, but this seems serious enough to
report here too.  I do not understand why Sage fails to factor n since
the documentation says that pari is the default, and pari can factor
this n (as above), however:

sage: n.factor(algorithm='pari')
2007193456621

but

sage: from sage.rings.factorint import factor_using_pari
sage: factor_using_pari(n)
[(1001797, 1), (2003593, 1)]

so something is going wrong before pari is getting called, perhaps a
primality test?

John

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