A teenage National Socialist allegedly listed targets for a "terror attack" in his own guerrilla warfare manual, a court heard.
The 16-year-old boy, from Durham, denies six terrorism offences.
He allegedly listed "means of attack" and "areas to attack" in the self-written manual, Manchester Crown Court heard.
Prosecutors said the boy also marked Adolf Hitler's birthday by calling him "a brave man to say the least".
Michelle Nelson QC, prosecuting, said that since about 2016 the boy had been "an adherent of a right-wing ideology" but "by late 2017 his view had hardened and he became an adherent of neo-Nazism".
In the course of internet searches, he allegedly looked for locations of synagogues and wrote of planning to conduct an arson spree targeting synagogues in the Durham area using Molotov cocktails, she told the jury.
The boy, who cannot be identified for legal reasons, allegedly visited websites on firearms, searched for knives and explosives, and was in communication with a gun auctioneer, Nelson said.
She told the court a handwritten note by the youth showed him taking on the ideology of "occult Nazism".
Among diary entries he wrote: "In journal format I hope to record events from now all the way to the inevitable race war."
The court heard he came to the attention of police in 2017 for so-called "racist tweets", but later continued searching for material on "lone wolf" attacks "despite telling detectives his Twitter activity was just for a laugh".
Marking Hitler's birthday in a diary entry, the boy said the german Führer was a "brave man to say the least … I one day hope to follow in his footsteps", the jury heard.
Jurors were told the boy's ideology was "wedded to the idea of accelerationism, that calls for the acceleration of the demise of liberal democracy… and that demise brought about by acts of violence".
The young defendant denies preparing acts of "terrorism, disseminating a terrorist publication, possessing an article for a terrorist purpose, and three counts of possessing terrorist documents".
The trial continues.