Block #894,929

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.

1.132 × 10⁹⁵(96-digit number)

11320120117121944518…14126027894523486379

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

1.132 × 10⁹⁵(96-digit number)

11320120117121944518…14126027894523486379

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.264 × 10⁹⁵(96-digit number)

22640240234243889036…28252055789046972759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.528 × 10⁹⁵(96-digit number)

45280480468487778073…56504111578093945519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.056 × 10⁹⁵(96-digit number)

90560960936975556146…13008223156187891039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.811 × 10⁹⁶(97-digit number)

18112192187395111229…26016446312375782079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.622 × 10⁹⁶(97-digit number)

36224384374790222458…52032892624751564159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.244 × 10⁹⁶(97-digit number)

72448768749580444917…04065785249503128319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.448 × 10⁹⁷(98-digit number)

14489753749916088983…08131570499006256639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.897 × 10⁹⁷(98-digit number)

28979507499832177966…16263140998012513279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.795 × 10⁹⁷(98-digit number)

57959014999664355933…32526281996025026559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

1.159 × 10⁹⁸(99-digit number)

11591802999932871186…65052563992050053119

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 #894,929

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