Block #2,784,781

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.

2.783 × 10⁹⁸(99-digit number)

27836047244046857610…04086453380771901439

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

2.783 × 10⁹⁸(99-digit number)

27836047244046857610…04086453380771901439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.567 × 10⁹⁸(99-digit number)

55672094488093715221…08172906761543802879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.113 × 10⁹⁹(100-digit number)

11134418897618743044…16345813523087605759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.226 × 10⁹⁹(100-digit number)

22268837795237486088…32691627046175211519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.453 × 10⁹⁹(100-digit number)

44537675590474972177…65383254092350423039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.907 × 10⁹⁹(100-digit number)

89075351180949944354…30766508184700846079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.781 × 10¹⁰⁰(101-digit number)

17815070236189988870…61533016369401692159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.563 × 10¹⁰⁰(101-digit number)

35630140472379977741…23066032738803384319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.126 × 10¹⁰⁰(101-digit number)

71260280944759955483…46132065477606768639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.425 × 10¹⁰¹(102-digit number)

14252056188951991096…92264130955213537279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.850 × 10¹⁰¹(102-digit number)

28504112377903982193…84528261910427074559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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

Block #2,784,781

Cookie Preferences