Block #857,325

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.

1.106 × 10⁹⁵(96-digit number)

11067606768007060239…32272096650251545279

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

1.106 × 10⁹⁵(96-digit number)

11067606768007060239…32272096650251545279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.213 × 10⁹⁵(96-digit number)

22135213536014120479…64544193300503090559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.427 × 10⁹⁵(96-digit number)

44270427072028240958…29088386601006181119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.854 × 10⁹⁵(96-digit number)

88540854144056481917…58176773202012362239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.770 × 10⁹⁶(97-digit number)

17708170828811296383…16353546404024724479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.541 × 10⁹⁶(97-digit number)

35416341657622592767…32707092808049448959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.083 × 10⁹⁶(97-digit number)

70832683315245185534…65414185616098897919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.416 × 10⁹⁷(98-digit number)

14166536663049037106…30828371232197795839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.833 × 10⁹⁷(98-digit number)

28333073326098074213…61656742464395591679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.666 × 10⁹⁷(98-digit number)

56666146652196148427…23313484928791183359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

1.133 × 10⁹⁸(99-digit number)

11333229330439229685…46626969857582366719

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 #857,325

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