Prime 𝑹𝑼𝑺𝑯

Mathematical Formula, Progression, & Analytics Explorer

MODE SYSTEM Dual Progression
MAX SPAN 1 ~ 193M+
SCALING METHOD Exponential Decay

βš™οΈ LIVE PROGRESSION SIMULATOR

15
75%
5
Active Phase: Phase 1
Classic Difficulty: 1.30x
Classic Max Spawn: 417
Classic Time Allocated: 10.00s
Zen Spawn Cap: 93,132
Base Point Output: 11 pts
Active Primes Pool: [2, 3, 5, 7]

πŸ” LIVE COMPUTATIONAL FORMULA STEP-LOG

πŸ† RANK ACCRUAL GAP MAP

Baseline rankings thresholds used for standard matching comparisons vs Zen thresholds.

C Tier Bracket 750 - 1,200 (Zen: 800 - 2k)
B Tier Bracket 1,200 - 1,600 (Zen: 2k - 5k)
A Tier Bracket 1,600 - 1,900 (Zen: 5k - 12.5k)
S / S+ Standard 1,900 - 2,250+ (Zen: 12.5k - 20k+)

πŸ“ GAMEPLAY ENGINE FORMULAS

The mechanical pacing of PrimeRush is driven by deterministic, stage-aware exponential and algebraic curves. Standard gameplay leverages segmented phases to ramp up numerical factor limits, whereas Zen Practice scaling operates on a smooth, custom exponential tier multiplier.

1. Classic Mode Points Calculation

The primary core points earned per prime factorization decay proportionally against elapsed time. It is driven by a sub-linear power equation of t^0.55, rewarding instant reactions heavily while preserving a respectable baseline for steady mathematical solvers:

Points = ⌈10 Γ— Difficulty Γ— (TimeRatio)^0.55βŒ‰

Where TimeRatio represents the remaining percentage of the active timer bar ($1.0 \to 0.0$).

2. Standard Progression Phases

Standard mode calculations segment gameplay based on n (total numbers defeated):

β–  Phase 1 (n ≀ 15 Numbers Defeated):

Spawns elements of pool [2, 3, 5, 7]

Difficulty (Scaling): D(n) = 1 + 0.02n

Spawn Cap: Cap(n) = 100 Γ— 1.1^n

Max Time: Time(n) = 8.5s + 0.1n


β–  Phase 2 (15 < n ≀ 30):

Spawns elements of pool [2, 3, 5, 7, 11, 13]

Difficulty (Scaling): D(n) = 0.7 + 0.04n

Spawn Cap: Cap(n) = 50 Γ— 1.1^n

Max Time: Time(n) = 7.0s + 0.2n


β–  Phase 3 (n > 30):

Spawns elements of pool [2, 3, 5, 7, ... 19, 23]

Difficulty (Scaling): D(n) = -1.1 + 0.1n

Spawn Cap: Cap(n) = 0.35 Γ— 1.25^n

Max Time: Time(n) = 13s + 0.5√(n - 30)

3. Zen Practice Mode Calculations

Zen Mode avoids temporal decay completely. To balance difficulty increments, it implements a tier-based scaling curve:

Base Spawn Cap = 100 Zen Cap(Tier) = 100 Γ— (1.25^5)^(Tier - 1) Point Factor = ⌈10 Γ— TierβŒ‰

Each difficulty level scales the overall numeric factor envelope by approximately ~3.05x compared to the previous Tier, capping at Tier 20 (Cap β‰ˆ 193,428,145).

πŸ”¬ ZEN PRACTICE POOL ALIGNMENTS

Pool Level 1: Primes: [2, 3, 5, 7]
Pool Level 2: Primes: [2, 3, 5, 7, 11, 13]
Pool Level 3: Primes: [2, 3, 5, 7, ... 19, 23]

SPAWNING CAPS SCALING METRIC

Comparing Classic Progression (n) limits against Zen Tier limits (Logarithmic Comparison)

⚑ POINT DECAY VS. TIME ELAPSED

Shows how point rewards diminish as standard timer counts down on the sub-linear curve.

⏳ ALLOCATED TIME SCALE BY PHASE

Demonstrates why high-phase limits grant longer timers for complex numbers.

πŸ“Š CLASSIC MODE PAYOUT MATRIX

Detailed computational overview of spawning, difficulty metrics, and relative score outputs across 60 progression stages.

Defeated (n) Spawn Cap Difficulty Max Time Payout 100% Payout 75% Payout 50% Payout 25%