Starting earlier this month, a slew of reports said Apple (Nasdaq: AAPL) was planning to release a new “low-cost iPhone” in mid-2013, but make the display larger, rather than smaller. This phone, which was said to be sold alongside an upgraded version of the iPhone 5 – presumably called either “iPhone 5S” or “iPhone 6” – was later listed as “iPhone Math” in a report from The China Times, although that name is likely a mistranslation.

But despite the growing number of reports about this new “iPhone Math,” a new report from iLounge’s Jeremy Horwitz says this iPhone model is only an early prototype, and is “certainly not expected” to be released in 2013.

“Addressing the so-called ‘iPhone Math’—hinted by one source as a mistranslation of ‘iPhone +’—we’ve been told that this is another new model and in early prototyping stages, certainly not expected in 2013,” Horwitz said. “It supposedly has a 4.7” screen, at least for the time being. It might never make it to market, and plenty could change before it does. Consider it Apple’s “just in case / Plan B” hedge against ever-growing Android phone screen sizes.

Sorting Out The iPhone Confusion

Talking about so many different iPhones can get confusing, so let’s clear a few things up:

Some reports mention the “iPhone Math” and “low-cost iPhone” as separate entities; however, considering how details of the two phones appear to be very similar, it’s possible that both devices are actually one and the same. Both phones are said to feature large, 4.8-inch screens, and it makes little sense to release two large, low-cost iPhones.

However, The Wall Street Journal and Bloomberg have both reported on Apple’s “low-cost” iPhone, and both of those reports say the low-cost iPhone would be smaller, not larger. In this case, Apple may be planning to release a smaller iPhone and a bigger iPhone, in addition to a newly upgraded iPhone 5 model.

Therefore, assuming the 4.8-inch iPhone Math is not the low-cost iPhone, Apple may have three new iPhones in the pipeline: The iPhone 5S or 6 (the true iPhone 5 successor), the low-cost iPhone (which could be smaller or larger), and the 4.8-inch iPhone Math.

Multiple reports mention three iPhones, including the original “iPhone Math” report from The China Times, as well as Horwitz. Topeka Markets analyst Brian White also said Apple would release iPhones in more colors and screen sizes in 2013.

The Low-Cost iPhone: Why The iPhone Math Must Wait

As Horwitz mentioned, the iPhone Math should be considered Apple’s “just in case / Plan B” iPhone model, just in case larger screened phones really do take off. However, as of now, Apple believes its best chance to break into new markets is to focus on improving its top-of-the-line iPhone, as well as introducing a new iPhone targeted at lower-income, emerging markets like China and India.

According to Horwitz, the low-cost iPhone is Apple’s priority, and “is indeed coming this year.”

“Also planned for a 2013 release is Apple’s ‘low-cost’ plastic-bodied iPhone, which is being developed with China Mobile in mind: The government-owned telecom company has over 700 million subscribers,” Horwitz said. “One of our sources claims that Apple’s iPhone prices remain too high for most mainland Chinese customers—the iPhone 5 hardware alone starts at $849 there, versus the iPhone 4 at $500, in a country where the average annual salary is around $3,000 per person). The source has said that mainland Chinese iPhone 5 sales are already tapering off as a result of the pricing, which is higher than in Hong Kong. A budget iPhone model would help sales in populous but underdeveloped countries to grow.”

Apple is clearly interested in selling its future iPhones – iPhone 5S, 6, Math, you name it – over China Mobile, the largest mobile telecommunications carrier in the world. Earlier this month during a trip to China, Apple CEO Tim Cook officially met with representatives with China Mobile to discuss “matters of cooperation,” according to Li Jun, a spokesman for China Mobile. DigiTimes said Apple’s plans to work with China Mobile include building a TD-LTE version of the iPhone, which would work on the carrier’s high-speed networks.

The appearance of the low-cost iPhone, according to DigiTimes, will reportedly feature “plastic for its chassis instead of reinforced glass or unibody metal,” which would help reduce the cost in producing the phone. DigiTimes also said the hybrid plastic and metal chassis would be at least semi-transparent, “with the internal metal parts being able to be seen from outside through special design. In many ways, the alleged design for this “iPhone Math” sounds like a mix between the iPhone 3GS from 2009 with its plastic enclosure, and the “Bondi blue” iMac from 1998, which was known for its bright, translucent plastic casing, letting users see the inside of their desktop computer for the first time.

Given the high priority of this low-cost iPhone – especially given how analysts and investors are disappointed with Apple’s first earnings report of the year – we can expect this low-cost iPhone, possibly called “iPhone 5S” or even “iPhone 6” if the true iPhone 5 successor takes another name – to release in mid- to late-2013.

iPhone 6: What We’ve Heard So Far

Completely separate from reports of an all-new iPhone (low-cost or “Math”), Apple is also expected to release an updated iPhone 5 this year, either called “iPhone 5S” or “iPhone 6.”

“The iPhone 5S is still months away from mass production, but our source suspects that the star feature will be an upgraded rear camera—perhaps featuring Sony’s 13-Megapixel sensor, plus the aforementioned flash upgrade—along with a processor bump,” Horwitz wrote in a separate article on Friday. “Current prototypes are codenamed N51 and N53, with July mentioned as the target date.”

Contrary to Horwitz’s report, while its details may be true, we’ve heard that the biggest focus of the iPhone 5S or 6 will actually be the home button, which is said to include an integrated fingerprint sensor to replace the need for usernames and passwords on the phone.

This fingerprint sensor makes a great deal of sense as an iPhone 6 feature: Unlike other smartphones with multiple bottoms on the bottom, the iPhone has only one mechanical button on its face, which makes it exceedingly easy and intuitive for users to find and use this feature. Furthermore, given Apple’s urgency to acquire Florida-based AuthenTec last July (as noted in the company’s own filing to the SEC), there’s an excellent chance that we’ll see this unique feature in the iPhone 5S or 6.

According to KGI Securities analyst Ming-Chi Kuo – one of the best at the business at predicting Apple’s product pipeline – the iPhone 5S or 6 will also feature a number of notable upgrades besides the fingerprint sensor, including a new A7 processor from Apple, and a new f2.0 aperture on the rear side camera with an advanced “smart LED flash” for enhanced photo-taking.

We’ve also heard that Apple is investing a great deal of time, energy and money on the display for its next-gen iPhone.

Jan. 3 report released by the China Times said Apple might switch to a "Touch On Display" panel currently in development at Taiwan-based Innolux Corp., which has reportedly been licensed to use Sharp's proprietary IGZO display technology.

Whether or not Apple chooses Innolux to make the next iPhone's screens, however, Apple is most likely going to feature Sharp's ultra-thin IGZO display technology in its next iPhone.

In late December, DigiTimes and Apple analyst Horace Dediu both mentioned Apple’s alleged investment in the ultra-thin IGZO displays produced by Sharp, predicting the inclusion of the technology in Apple’s next batch of iOS devices, including iPhones and iPads. Dediu also pointed to Apple’s recent $2.3 billion investment in “product tooling, manufacturing process equipment and infrastructure,” believing the cash was used to help bail out Sharp, which had been in financial straits in 2012. Sharp is reportedly going “all in” on IGZO technology, so it’s possible Apple saved Sharp to leverage its investment in the next generation of displays.

IGZO display technology is not only thin and tough, but it can even handle higher screen densities than Apple’s Retina display, which is visually stunning on its own. IGZO displays can reportedly handle display densities north of 330 ppi; for a quick comparison, the new iPad 4 can only achieve 264 ppi.

One of the advantages of IGZO display technology is its lower power consumption. Most Apple products, from the iPhone 5 to the iPad 4, require cartoonishly big batteries to achieve just eight hours of power -- this is because current-gen Retina displays are extremely power hungry. If Apple wanted its iPhone 6 to not only last longer during the day but also charge faster when plugged in, IGZO seems to be the way to go for the next generation of iOS devices.

Giving credence to these rumors, Taiwan-based AU Optronics (AUO) reportedly plans to develop a Retina display for the next-generation iPad Mini, which may require IGZO technology to make such a Retina display feasible.

Besides these display rumors, we haven't heard too many other legitimate reports, but we have, however, noticed a few interesting patents: A patent filed in March but published in September described tactile keyboards, flexible displays and laser microphones and speakers built into an iPhone, designed to conform to the user's needs. Flexible displays would allow for easier holding and typing, while the highly advanced tactile screens would create buttons when needed so users can feel "keyboard" letters as they type, or touch the topography on Apple's Maps. 

It's wishful thinking that Apple would include all these technologies in this year’s iPhone 5S or 6, rather implement them over time, but it's certainly fun to think about.

Apple sold 47.8 million iPhones and 22.9 million iPads in Q1 2013.