We solve, analytically and numerically, a gap equation in parity invariant QED3 in the presence of an infrared cutoff µ and derive an expression for the critical fermion number Nc as a function of µ. We argue that this dependence of Nc on the infrared scale might solve the discrepancy between continuum Schwinger-Dyson equations studies and lattice simulations of QED3.PACS numbers: 11.10. Kk, 11.30.Qc, 12.20.Ds Parity invariant quantum electrodynamics in 2+1 dimensions with N flavors of four-component massless fermions (QED 3 ) [1] has been attracting a lot of interest for almost two decades. While it was often regarded as a nice polygon for studying nonperturbative phenomena in gauge field theories, such as dynamical mass generation, recently the model has found applications in condensed matter physics, in particular in high-T c superconductivity [2].QED 3 is ultraviolet finite and has a built-in intrinsic mass scale given by the dimensionful gauge coupling e, or α = e 2 N/8, which plays a role similar to the Λ scale parameter in QCD. In the leading order in 1/N expansion, it was found that at large momenta (p ≫ α) the effective coupling between fermions and gauge bosons vanishes (asymptotic freedom) whereas it has a finite value or infrared stable fixed point at p ≪ α [3]. This behavior was shown to be robust against the introduction of higher order 1/N corrections [4,5]. Studies of the gap equation for a fermion dynamical mass in the leading order in the 1/N expansion have shown that massless QED 3 exhibits chiral symmetry breaking whenever the number of fermion species N is less than some critical value N c , which is estimated to be in the region 3 < N c < 5 (N c = 32/π 2 ≃ 3.2 in the simplest ladder approximation [6]). A renormalization group analysis gives 3 < N c < 4 [7]. Below such a critical N c , the U (2N ) flavor symmetry is broken down to U (N ) × U (N ), the fermions acquire a dynamical mass, and 2N 2 Goldstone bosons appear; for N > N c the particle spectrum of the model consists of interacting massless fermions and a photon. In addition, it was argued that the dynamical symmetry breaking phase transition at N = N c is a conformal phase transition [8,9]. The last one is characterized by a scaling function for the dynamical fermion mass with an essential singularity [6,8].On the other hand, there is an argument due to Appelquist et al. [10] that N c ≤ 3/2. The argument is based on the inequality f IR ≤ f UV where f is the thermodynamic free energy which is estimated in both infrared and ultraviolet regimes by counting massless degrees of freedom.The above-described version of QED 3 , the so-called parity invariant noncompact version, was studied on a lattice [11]. Recent lattice simulations of QED 3 with N ≥ 2 have found no decisive signal for chiral symmetry breaking [12]. In particular, for N = 2, Ref. [12] reports an upper bound for the chiral condensate ψ ψ to be of order 5 × 10 −5 in units of e 4 . We recall that for quenched, N = 0, QED 3 both numerical [13] and analytical [14] studies hav...