[Math] Real-world example for Diffie–Hellman key exchange

Question

I read in Wikipedia about the Diffie–Hellman key exchange.
But i can't imagine numbers which are hard to guess.

Can anybody give me a real-world example for $p$, $g$ and the two random secrets?

Answer 1

I am Bob and I am communicating with Alice. You are Eve, the eavesdropper and you see the following information being passed between us.

$p$ = a 396 digit prime 315791951375393537137595555337555955191395351995195751755791151795317131135377351919777977373317997317733397199751739199735799971153399111973979977771537137371797357935195531355957399953977139577337393111951779135151171355371173379337573915193973715113971779315731713793579595533511197399993313719939759551175175337795317333957313779755351991151933337157555517575773115995775199513553337335137111

$g$ = 5

$g^a \mod p$ = 27489633325073800398775665555817886420250962668110351939566023888497836125868152406573384812160988816636135839671600830972123154326698347543908237984222952075526254924036242003399678149299821208547691422947419851811974028751045560581548575054043995970503234125889791605774889110477621403114012112713190957314561511096280698589221374817602716179951101187316281123669357781523803509664317497207729

$g^b \mod p$ = 1871328666565825995546798366128332313007950715331716749713204590388482544710311757501721471367857473733174282285058381076423826262539615001751155796241435075482428300917592530410990583546909080238556317378367406354698458062808098314556896127603125072486660646729701592117222647853144199702370081278435240604316086143749700366105405028431580266698489313733272288229202699113269909480645581599706251

and now you tell me what is the secret that Alice and I share $g^{ab} \mod p$.