Block #55,462

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/17/2013, 1:48:25 AM · Difficulty 8.9421 · 6,760,486 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

39228e72abecd54613f3be15235203d981d8fdf2e028552b7666a6284e3c9785

View on Chainz ↗

Height

#55,462

Difficulty

8.942083

Transactions

Size

479 B

Version

Bits

08f12c59

Nonce

323

Timestamp

7/17/2013, 1:48:25 AM

Confirmations

6,760,486

Mined by

⛏️ P2SHAaZQX24tfR5Kkc2ZASqC3mPxnQczgvbcUw

Merkle Root

6dd164e151ee82be5b90d1742a7427a1dfd7b64c1c71862c68d5000cd7a1ae50

Transactions (2)

Coinbase9c7bdb5971c08d…bda9aa6206436e

1 in → 1 out12.5000 XPM110 B

AaZQX24t…czgvbcUw

1d03814e2cbc7a…22aeb52cf6cee4

2 in → 1 out25.2600 XPM272 B

AccN9Axq…tJCNZ8bv

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.

1.496 × 10¹¹¹(112-digit number)

14966245004063265099…35724904427929138499

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

1.496 × 10¹¹¹(112-digit number)

14966245004063265099…35724904427929138499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.993 × 10¹¹¹(112-digit number)

29932490008126530198…71449808855858276999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.986 × 10¹¹¹(112-digit number)

59864980016253060396…42899617711716553999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.197 × 10¹¹²(113-digit number)

11972996003250612079…85799235423433107999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.394 × 10¹¹²(113-digit number)

23945992006501224158…71598470846866215999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.789 × 10¹¹²(113-digit number)

47891984013002448317…43196941693732431999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.578 × 10¹¹²(113-digit number)

95783968026004896634…86393883387464863999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.915 × 10¹¹³(114-digit number)

19156793605200979326…72787766774929727999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #55,462

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