Since the magical number is seven for Horcruxes, and Voldemort made Harry unintentionally then there must be an eighth right...???
Voldemort did not want to make seven horcruxes. He wanted to split his soul into seven parts, six of them would be protected by horcruxes and the seventh would reside in his body.
In The Half Blood Prince we learn of Voldemort's plan of splitting his soul into seven pieces:
Wouldn't it be better, make you stronger, to have your soul in more pieces, I mean, for instance, isn't seven the most powerfully magical number, wouldn't seven - ?
Slughorn responds:
... bad enough to divide the soul... but to rip it into seven pieces...
Finally, Dumbledore corrects Harry's assumption of seven horcruxes:
But firstly no, Harry, not seven horcruxes: six. The seventh part of his soul, however maimed, resides in his regenerated body. That was the part of him that lived a spectral existence for so many years during his exile.
The Dark Lord only needed to have one piece of soul outside of his body to keep him alive. As long as he had at least one Horcrux remaining, it would've ensured he couldn’t die.
“Well, you split your soul, you see,’ said Slughorn, ‘and hide part of it in an object outside the body. Then, even if one’s body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged. But, of course, existence in such a form …”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
If he’d had any more Horcruxes, when Harry caused his Killing Curse to rebound, he’d have escaped in a spectral form, and that spectral form would have first appeared right where his body was killed. That’s what happened the last time he was hit by a rebounding Killing Curse but kept alive by his Horcruxes - his body was killed, but his spectral form was there in the Potters’ house.
“He pointed the wand very carefully into the boy’s face: he wanted to see it happen, the destruction of this one, inexplicable danger. The child began to cry: it had seen that he was not James. He did not like it crying, he had never been able to stomach the small ones’ whining in the orphanage –
‘Avada Kedavra!’
And then he broke: he was nothing, nothing but pain and terror, and he must hide himself, not here in the rubble of the ruined house, where the child was trapped and screaming, but far away … far away …”
- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)
However, the Dark Lord dies, witnessed by Harry and several others, and no spirit form of him is seen near his body when it died, as would have happened if he had any Horcruxes remaining.
“And Harry, with the unerring skill of the Seeker, caught the wand in his free hand as Voldemort fell backwards, arms splayed, the slit pupils of the scarlet eyes rolling upwards. Tom Riddle hit the floor with a mundane finality, his body feeble and shrunken, the white hands empty, the snake-like face vacant and unknowing. Voldemort was dead, killed by his own rebounding curse, and Harry stood with two wands in his hand, staring down at his enemy’s shell.
One shivering second of silence, the shock of the moment suspended: and then the tumult broke around Harry as the screams and the cheers and the roars of the watchers rent the air.”
- Harry Potter and the Deathly Hallows, Chapter 36 (The Flaw in the Plan)
Therefore, all the Dark Lord’s Horcruxes would’ve had to be destroyed by then, since he clearly died with no spectral form of him escaping from his body where he died.
Though it’s made clear when the Dark Lord died that all his Horcruxes were destroyed, he’d only ever intended to make six. Harry also originally thought the Dark Lord had made seven Horcruxes, but Dumbledore corrects him, explaining the Dark Lord’s seven-part soul included the ‘main’ piece.
“He made seven Horcruxes?’ said Harry, horror-struck, while several of the portraits on the walls made similar noises of shock and outrage. ‘But they could be anywhere in the world – hidden – buried or invisible –’
‘I am glad to see you appreciate the magnitude of the problem,’ said Dumbledore calmly. ‘But firstly, no, Harry, not seven Horcruxes: six. The seventh part of his soul, however maimed, resides inside his regenerated body. That was the part of him that lived a spectral existence for so many years during his exile; without that, he has no self at all. That seventh piece of soul will be the last that anybody wishing to kill Voldemort must attack – the piece that lives in his body.”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
The Dark Lord meant to have his soul in seven pieces in all, including the main one that wasn’t in a Horcrux. In addition, Dumbledore also says that the piece that lives in the Dark Lord’s body would have to be the last one to be killed. This further shows all the Horcruxes were destroyed before the Dark Lord died, as Dumbledore likely meant that the main piece couldn’t be killed until they were.
In the Half-Blood Prince, we learn, after Harry retrieves the real memory from Professor Slughorn, exactly what Riddle/Voldemort's intentions were in creating 7 horcruxes. This begins the discussion of what the horcruxes could be, having already identified and destroyed the diary and the ring. During this exchange, Dumbledore suspects that Voldemort had not yet created a 7th horcrux, but was instead planning on using the murder of Harry to create the 7th and final horcrux. As we all know, Voldemort was unable to kill Harry as a baby, and as a result, his body was destroyed, leaving him unable to create the horcurx as intended. Therefore, there would be no 8th horcrux floating around.
Sorry that I do not have actual dialog from the book to cite, I do not have the books with me at the moment, and will update this answer as soon as I can.
It was never stated that Voldemort intended to make 7 horcruxes, only that Voldemort's soul was split into 7 pieces... Voldemort only intended to make 6 horcruxes, with his own body housing the 7th split piece. Harry was the accidental 7th horcrux. There are some who seem to deny that Harry is a horcrux... that he just, as Rowling describes, "houses" a horcrux in his scar. But just as a locket is a horcrux, even though it only " houses" a horcrux... Harry fits the definition of horcrux even though he only houses a piece of Voldemort's soul.
