Block #252,911

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/9/2013, 8:19:10 PM · Difficulty 9.9717 · 6,552,242 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c554643f27061b983792010180703036747c2f494959707f1681de4938b0b27f

View on Chainz ↗

Height

#252,911

Difficulty

9.971680

Transactions

Size

1.74 KB

Version

Bits

09f8c000

Nonce

15,510

Timestamp

11/9/2013, 8:19:10 PM

Confirmations

6,552,242

Mined by

⛏️ aR~Ae5PDmtajEbidfVuPJ9TF2ksg6co6zVVJQ

Merkle Root

1ea65f4b0f25b647fad20b7e00cb9f299c915c63a7c71043f899a783198d1d16

Transactions (1)

Coinbase1ea65f4b0f25b6…99a783198d1d16

1 in → 48 out10.0200 XPM1.66 KB

Ae5PDmta…co6zVVJQ AScCYXya…oAz38X3p AeNjg8HA…9AkdpcSC AKDTDDtx…iqvw9cdY ANo4YY1x…vnsPRDSU

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.

2.843 × 10⁹⁷(98-digit number)

28436836962622290423…99019940495927610239

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

2.843 × 10⁹⁷(98-digit number)

28436836962622290423…99019940495927610239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.687 × 10⁹⁷(98-digit number)

56873673925244580846…98039880991855220479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.137 × 10⁹⁸(99-digit number)

11374734785048916169…96079761983710440959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.274 × 10⁹⁸(99-digit number)

22749469570097832338…92159523967420881919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.549 × 10⁹⁸(99-digit number)

45498939140195664677…84319047934841763839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.099 × 10⁹⁸(99-digit number)

90997878280391329355…68638095869683527679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.819 × 10⁹⁹(100-digit number)

18199575656078265871…37276191739367055359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.639 × 10⁹⁹(100-digit number)

36399151312156531742…74552383478734110719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.279 × 10⁹⁹(100-digit number)

72798302624313063484…49104766957468221439

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