Snopes: Luckily for those fond of their Granny Smiths, the body can detoxify cyanide in small doses, and the number of apple seeds it takes to pack a lethal punch is therefore so huge that even the most dedicated of apple eaters is extremely unlikely to ingest enough pips to cause any harm. Yet those who have heard apple seeds house a poison (usually remembered as arsenic, a quite different though equally deadly compound) cling to the frightening belief swallowing a small number of pips spells instant death.

I can't find an estimate right now, but you would have to eat at least a big handful of seeds, while making sure you grind them up in your mouth. It's not wise to worry about this.