Block #80,446

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/24/2013, 4:05:36 AM · Difficulty 9.2497 · 6,723,301 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b5d25ebc88a37e70df68fa69b47aaee632b3ed4eedfeb212c2e4125954f26b52

View on Chainz ↗

Height

#80,446

Difficulty

9.249688

Transactions

Size

213 B

Version

Bits

093feb95

Nonce

2,006

Timestamp

7/24/2013, 4:05:36 AM

Confirmations

6,723,301

Mined by

⛏️ P2SHAUKHL3eLyEnFHPVueP1XSDJ5QKskSF7HRM

Merkle Root

20771eb2c65b815316844943170125ca6677bd5c81b5669bca450609aba789b6

Transactions (1)

Coinbase20771eb2c65b81…450609aba789b6

1 in → 1 out11.6700 XPM112 B

AUKHL3eL…skSF7HRM

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.

1.710 × 10¹²²(123-digit number)

17108426762951503414…10310928549857887999

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

1.710 × 10¹²²(123-digit number)

17108426762951503414…10310928549857887999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.421 × 10¹²²(123-digit number)

34216853525903006828…20621857099715775999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.843 × 10¹²²(123-digit number)

68433707051806013657…41243714199431551999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.368 × 10¹²³(124-digit number)

13686741410361202731…82487428398863103999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.737 × 10¹²³(124-digit number)

27373482820722405462…64974856797726207999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.474 × 10¹²³(124-digit number)

54746965641444810925…29949713595452415999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.094 × 10¹²⁴(125-digit number)

10949393128288962185…59899427190904831999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.189 × 10¹²⁴(125-digit number)

21898786256577924370…19798854381809663999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.379 × 10¹²⁴(125-digit number)

43797572513155848740…39597708763619327999

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