Block #225,225

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/24/2013, 8:24:07 AM · Difficulty 9.9366 · 6,579,815 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5aa3ddf4d38cb0f1f9174a85959cb8032d8e978fd2173e52b8068809bfa97a70

View on Chainz ↗

Height

#225,225

Difficulty

9.936642

Transactions

Size

1.24 KB

Version

Bits

09efc7cb

Nonce

468,933

Timestamp

10/24/2013, 8:24:07 AM

Confirmations

6,579,815

Mined by

⛏️ oRhAKFMENK8Y83ntTmGeVC63vAJZ8b6knxLfH

Merkle Root

5632ee6270d60b29af4bf7752c08c41dfdda952a95c988a24fb544df7bea58b4

Transactions (1)

Coinbase5632ee6270d60b…b544df7bea58b4

1 in → 33 out10.0897 XPM1.16 KB

AKFMENK8…b6knxLfH ANuKx9Ke…wm7nrBRq ALFWpHxd…zhX7LjhL AJaGRnaj…iCHGoy6E AaSot6r4…DjoWHEUX

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.

7.266 × 10⁹³(94-digit number)

72661394173262155935…82944899560723887999

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

7.266 × 10⁹³(94-digit number)

72661394173262155935…82944899560723887999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.453 × 10⁹⁴(95-digit number)

14532278834652431187…65889799121447775999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.906 × 10⁹⁴(95-digit number)

29064557669304862374…31779598242895551999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.812 × 10⁹⁴(95-digit number)

58129115338609724748…63559196485791103999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.162 × 10⁹⁵(96-digit number)

11625823067721944949…27118392971582207999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.325 × 10⁹⁵(96-digit number)

23251646135443889899…54236785943164415999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.650 × 10⁹⁵(96-digit number)

46503292270887779798…08473571886328831999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.300 × 10⁹⁵(96-digit number)

93006584541775559597…16947143772657663999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.860 × 10⁹⁶(97-digit number)

18601316908355111919…33894287545315327999

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