Block #862,361

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.

2.353 × 10⁹⁵(96-digit number)

23532939521332075228…03081683114713042801

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

2.353 × 10⁹⁵(96-digit number)

23532939521332075228…03081683114713042801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.706 × 10⁹⁵(96-digit number)

47065879042664150457…06163366229426085601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.413 × 10⁹⁵(96-digit number)

94131758085328300915…12326732458852171201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.882 × 10⁹⁶(97-digit number)

18826351617065660183…24653464917704342401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.765 × 10⁹⁶(97-digit number)

37652703234131320366…49306929835408684801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.530 × 10⁹⁶(97-digit number)

75305406468262640732…98613859670817369601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.506 × 10⁹⁷(98-digit number)

15061081293652528146…97227719341634739201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.012 × 10⁹⁷(98-digit number)

30122162587305056293…94455438683269478401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.024 × 10⁹⁷(98-digit number)

60244325174610112586…88910877366538956801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.204 × 10⁹⁸(99-digit number)

12048865034922022517…77821754733077913601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.409 × 10⁹⁸(99-digit number)

24097730069844045034…55643509466155827201

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 Second 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 2CC formula:

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

Cross-reference on Chainz Explorer

Block #862,361

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