Block #180,452

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/25/2013, 8:20:41 PM · Difficulty 9.8617 · 6,615,611 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

665a908edb74aff1320841eefa3c23cb09f51e859c8b983d8011f0f5ed2a7615

View on Chainz ↗

Height

#180,452

Difficulty

9.861671

Transactions

Size

3.05 KB

Version

Bits

09dc967a

Nonce

537,067

Timestamp

9/25/2013, 8:20:41 PM

Confirmations

6,615,611

Mined by

⛏️ P2SHANsvDN5KDUBF83BQczFTri757NjwzDHo7V

Merkle Root

0b5a8cb99817e2fce3c67675806bf293d19ae6b2aa8fe6b08fa2ccaa221cb142

Transactions (3)

Coinbase2cbc15cb7cbe9a…1df603d8ba6d64

1 in → 1 out10.3100 XPM109 B

ANsvDN5K…jwzDHo7V

657be799fd96ad…779a7f453bc6aa

23 in → 1 out228.3000 XPM2.64 KB

APWYD1B3…fg6JkRZY

4c52d7c28ffe08…75253fdac29eec

1 in → 2 out3.2075 XPM226 B

AG28eyJk…CQEXrtgP AdWp2YRv…FDtt217a

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.

1.122 × 10⁹³(94-digit number)

11222641156147556817…87997685391923604599

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

1.122 × 10⁹³(94-digit number)

11222641156147556817…87997685391923604599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.244 × 10⁹³(94-digit number)

22445282312295113635…75995370783847209199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.489 × 10⁹³(94-digit number)

44890564624590227270…51990741567694418399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.978 × 10⁹³(94-digit number)

89781129249180454540…03981483135388836799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.795 × 10⁹⁴(95-digit number)

17956225849836090908…07962966270777673599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.591 × 10⁹⁴(95-digit number)

35912451699672181816…15925932541555347199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.182 × 10⁹⁴(95-digit number)

71824903399344363632…31851865083110694399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.436 × 10⁹⁵(96-digit number)

14364980679868872726…63703730166221388799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.872 × 10⁹⁵(96-digit number)

28729961359737745453…27407460332442777599

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