Block #455,336

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/22/2014, 12:26:31 PM · Difficulty 10.4075 · 6,352,771 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1be31b55fbb35e1643e7cf92b6dc50ed2e98d54816362e1afd2e40643b20e0d0

View on Chainz ↗

Height

#455,336

Difficulty

10.407537

Transactions

Size

935 B

Version

Bits

0a685451

Nonce

82,299

Timestamp

3/22/2014, 12:26:31 PM

Confirmations

6,352,771

Mined by

⛏️ aS-lAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

482a6ce2697595eec39825b593da0bec0d71f899af18cfe196ad2c5928b04e79

Transactions (1)

Coinbase482a6ce2697595…ad2c5928b04e79

1 in → 23 out9.2200 XPM845 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq AQwRN8bE…V8PsTcY9

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.

3.633 × 10⁹³(94-digit number)

36333363740431398673…80894626532179563519

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

3.633 × 10⁹³(94-digit number)

36333363740431398673…80894626532179563519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.266 × 10⁹³(94-digit number)

72666727480862797347…61789253064359127039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.453 × 10⁹⁴(95-digit number)

14533345496172559469…23578506128718254079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.906 × 10⁹⁴(95-digit number)

29066690992345118939…47157012257436508159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.813 × 10⁹⁴(95-digit number)

58133381984690237878…94314024514873016319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.162 × 10⁹⁵(96-digit number)

11626676396938047575…88628049029746032639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.325 × 10⁹⁵(96-digit number)

23253352793876095151…77256098059492065279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.650 × 10⁹⁵(96-digit number)

46506705587752190302…54512196118984130559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.301 × 10⁹⁵(96-digit number)

93013411175504380604…09024392237968261119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.860 × 10⁹⁶(97-digit number)

18602682235100876120…18048784475936522239

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 #455,336

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