Hello, I was digging (possible) expressions for mass ratios of fundamental particles and found 3 which I find amusing. The first one is for Mn/Mp, the neutron/proton ratio which is 1.00137841917 (45) (codata 2010). the expression is 8/27 ( 5/cos(Pi/15) - sqrt(3)). = 1.0013784197796... The other one is for Mp/Me, proton/electron ratio which is 1836.15267261 (75) 1 5 1 1/5 -------- + 6 Pi + 1/5 -------- = 1836.1526799668615... cosh(Pi) sinh(Pi) or lprinted : 1/5/cosh(Pi)+6*Pi^5+1/5/sinh(Pi); very symmetric , it reminds me of the value that R. Feynmann gave in the 60's of 6*Pi^5 but a bit far from the real value. A simple analysis of the error would reject that expression, it is 9 times the standard error. But, ? , something is missing perhaps, another symmetric term (or 2) ? Another one which does respect the error term would be -((2000 (-12 + Sin[\[Pi]/60]))/(10 + 3 Cos[\[Pi]/60])) = 1838.683664899565... very close to the real value of 1838.6836605(11) also in the CODATA 2010 values. In this case : error term is ok but the complexity, too high ? These are the only ones among millions of expressions found using the table of 13.155 billion entries. NOTE : these are just guesses, they have no pretension of exactness or physical reality, they are simply the best and simplest expressions that satisfies the error term and/or the complexity so far. Unless someone have another educated guess. ? Best regards, Simon Plouffe