Block #361,552

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.

1.146 × 10¹⁰¹(102-digit number)

11467203360546865036…69263289400841743361

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

1.146 × 10¹⁰¹(102-digit number)

11467203360546865036…69263289400841743361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.293 × 10¹⁰¹(102-digit number)

22934406721093730073…38526578801683486721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.586 × 10¹⁰¹(102-digit number)

45868813442187460146…77053157603366973441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.173 × 10¹⁰¹(102-digit number)

91737626884374920292…54106315206733946881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.834 × 10¹⁰²(103-digit number)

18347525376874984058…08212630413467893761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.669 × 10¹⁰²(103-digit number)

36695050753749968116…16425260826935787521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.339 × 10¹⁰²(103-digit number)

73390101507499936233…32850521653871575041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.467 × 10¹⁰³(104-digit number)

14678020301499987246…65701043307743150081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.935 × 10¹⁰³(104-digit number)

29356040602999974493…31402086615486300161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.871 × 10¹⁰³(104-digit number)

58712081205999948986…62804173230972600321

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #361,552

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