Block #62,526

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/18/2013, 7:54:43 PM · Difficulty 8.9766 · 6,753,329 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fc43486f13ad05dd7b7d39a5d06f6a76a728431929bb379ee040149722c8053f

View on Chainz ↗

Height

#62,526

Difficulty

8.976606

Transactions

Size

199 B

Version

Bits

08fa02d5

Nonce

404

Timestamp

7/18/2013, 7:54:43 PM

Confirmations

6,753,329

Mined by

⛏️ P2SHALXjrugCYbt29xU2ER2ywowb9GhByoynjy

Merkle Root

03c1d2b9bf88a2a5bed7dcc3a1402cb234e1197499d996c9ab0d4467411ecd01

Transactions (1)

Coinbase03c1d2b9bf88a2…0d4467411ecd01

1 in → 1 out12.3900 XPM110 B

ALXjrugC…hByoynjy

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.

1.753 × 10⁹¹(92-digit number)

17534959782606840497…21237345127470500489

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

1.753 × 10⁹¹(92-digit number)

17534959782606840497…21237345127470500489

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.506 × 10⁹¹(92-digit number)

35069919565213680994…42474690254941000979

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.013 × 10⁹¹(92-digit number)

70139839130427361989…84949380509882001959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.402 × 10⁹²(93-digit number)

14027967826085472397…69898761019764003919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.805 × 10⁹²(93-digit number)

28055935652170944795…39797522039528007839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.611 × 10⁹²(93-digit number)

56111871304341889591…79595044079056015679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.122 × 10⁹³(94-digit number)

11222374260868377918…59190088158112031359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.244 × 10⁹³(94-digit number)

22444748521736755836…18380176316224062719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.488 × 10⁹³(94-digit number)

44889497043473511673…36760352632448125439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #62,526

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