Block #52,417

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/16/2013, 10:14:59 AM · Difficulty 8.9118 · 6,755,041 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fe320f535ff6cf7b41b83a4fcc0a1943076bbfcb6c13567d31939fc54e80f3de

View on Chainz ↗

Height

#52,417

Difficulty

8.911841

Transactions

Size

204 B

Version

Bits

08e96e6c

Nonce

224

Timestamp

7/16/2013, 10:14:59 AM

Confirmations

6,755,041

Mined by

⛏️ P2SHAZFLjZyKhpsWbsMjp8AMyFndfGUdnxrPbb

Merkle Root

217aebb49c887cc79a70548b5fcb8e2a1f8d6dcc867a643a96d18d98a11d46b5

Transactions (1)

Coinbase217aebb49c887c…d18d98a11d46b5

1 in → 1 out12.5700 XPM110 B

AZFLjZyK…UdnxrPbb

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.

3.072 × 10¹⁰⁵(106-digit number)

30723266036902840695…33104052319262474239

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

3.072 × 10¹⁰⁵(106-digit number)

30723266036902840695…33104052319262474239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.144 × 10¹⁰⁵(106-digit number)

61446532073805681390…66208104638524948479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.228 × 10¹⁰⁶(107-digit number)

12289306414761136278…32416209277049896959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.457 × 10¹⁰⁶(107-digit number)

24578612829522272556…64832418554099793919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.915 × 10¹⁰⁶(107-digit number)

49157225659044545112…29664837108199587839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.831 × 10¹⁰⁶(107-digit number)

98314451318089090224…59329674216399175679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.966 × 10¹⁰⁷(108-digit number)

19662890263617818044…18659348432798351359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.932 × 10¹⁰⁷(108-digit number)

39325780527235636089…37318696865596702719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.865 × 10¹⁰⁷(108-digit number)

78651561054471272179…74637393731193405439

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 #52,417

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