Block #245,200

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.609 × 10⁹⁹(100-digit number)

16092792845377924984…68510600648030774459

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

1.609 × 10⁹⁹(100-digit number)

16092792845377924984…68510600648030774459

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.218 × 10⁹⁹(100-digit number)

32185585690755849969…37021201296061548919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.437 × 10⁹⁹(100-digit number)

64371171381511699938…74042402592123097839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.287 × 10¹⁰⁰(101-digit number)

12874234276302339987…48084805184246195679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.574 × 10¹⁰⁰(101-digit number)

25748468552604679975…96169610368492391359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.149 × 10¹⁰⁰(101-digit number)

51496937105209359950…92339220736984782719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.029 × 10¹⁰¹(102-digit number)

10299387421041871990…84678441473969565439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.059 × 10¹⁰¹(102-digit number)

20598774842083743980…69356882947939130879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.119 × 10¹⁰¹(102-digit number)

41197549684167487960…38713765895878261759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer