Block #275,450

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/26/2013, 5:15:11 PM · Difficulty 9.9608 · 6,536,798 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

83b9115ea1cc5e3712178ab94d29fc1f906a709e97321dda02caefea2b3c82a4

View on Chainz ↗

Height

#275,450

Difficulty

9.960806

Transactions

Size

798 B

Version

Bits

09f5f760

Nonce

54,318

Timestamp

11/26/2013, 5:15:11 PM

Confirmations

6,536,798

Mined by

⛏️ 3aRAe58nAEbon8TkEL3qBwA5Y17zVGFUA15fv

Merkle Root

8bcca8cceede7ab148568f02a72cfcd1734c21090ee768c9bb3beaa30ae74881

Transactions (1)

Coinbase8bcca8cceede7a…3beaa30ae74881

1 in → 19 out10.0600 XPM709 B

Ae58nAEb…GFUA15fv ARbAfyVV…c4ekwYz6 Abv8pzf1…t4zPXDTV AMTsAvuY…U6q9Qns4 AFxYnWJi…bUMAd5Gt

Prime Chain Origin

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.

5.507 × 10⁹¹(92-digit number)

55075688920139340423…02104222638550965489

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

5.507 × 10⁹¹(92-digit number)

55075688920139340423…02104222638550965489

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.101 × 10⁹²(93-digit number)

11015137784027868084…04208445277101930979

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.203 × 10⁹²(93-digit number)

22030275568055736169…08416890554203861959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.406 × 10⁹²(93-digit number)

44060551136111472338…16833781108407723919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.812 × 10⁹²(93-digit number)

88121102272222944677…33667562216815447839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.762 × 10⁹³(94-digit number)

17624220454444588935…67335124433630895679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.524 × 10⁹³(94-digit number)

35248440908889177870…34670248867261791359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.049 × 10⁹³(94-digit number)

70496881817778355741…69340497734523582719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.409 × 10⁹⁴(95-digit number)

14099376363555671148…38680995469047165439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.819 × 10⁹⁴(95-digit number)

28198752727111342296…77361990938094330879

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #275,450

Cookie Preferences