Using Boost multiprecisin (BTW I used Archmedes' algorithm using harmonic and geometric means to compute to yuge accuracy). It looks like an integer indeed. I suspect normal double version can't handle it.

en.wikipedia.org

The code is in my C++ 2018 book.

3.14159

3.14159265358979

3.1415926535897932384626433832795028841971693993751

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068

Magic integer

262537412640768247.5713554167712991078224994808335372233815523938265062293007555722918377393427009604

** new pi **

43062804053610537.76967918899868909101406635211473906962110080227236871410401309739269354850048499291

262537412640331140.2414762438347411580194256137678722715167156310740143682592730682027487333077100697

262537412640768743.9999996020009502189844234272239222590573356870428627795435819912010134976105000139

262537412640768743.9999999999992500722352208406573853349085723538921505547272499473446300146691943047

262537412640768743.9999999999992500725971981856885501373788693619910561648975035470439632733387529961

262537412640768743.9999999999992500725971981856888793538563370375702207140675390317660143219099661867

262537412640768743.9999999999992500725971981856888793538563373369908627072650888907161383163144617668

262537412640768743.9999999999992500725971981856888793538563373369908627075374103782104002351685521337

262537412640768743.9999999999992500725971981856888793538563373369908627075374103782106479101186070877

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

Normal double precision 262537412640768256 (looks like a 'wrong' integer).

Edit: I suspect the last case gives an FE_OVERFLOW error... haven't checked it.