Block #243,639

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/4/2013, 10:05:44 AM · Difficulty 9.9618 · 6,572,583 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5456f09350f3a489a504dc31cc2b86d04a4c3df36c4e4a873a8fe716aaeafd86

View on Chainz ↗

Height

#243,639

Difficulty

9.961773

Transactions

Size

1.54 KB

Version

Bits

09f636c7

Nonce

58,948

Timestamp

11/4/2013, 10:05:44 AM

Confirmations

6,572,583

Mined by

⛏️ RwqnANuKx9Kemb4q2j6b7vjmfuKrAuwm7nrBRq

Merkle Root

3dd13267bdc523fe980e92d27f10d9a17f02fc148d8faf511885b6b562b5d231

Transactions (1)

Coinbase3dd13267bdc523…85b6b562b5d231

1 in → 42 out10.0400 XPM1.46 KB

ANuKx9Ke…wm7nrBRq ATKK7iFz…wZm46KN1 ALFWpHxd…zhX7LjhL Acs9SHrk…QJSB8SFG APVGazMT…cDCk2nwA

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.

9.467 × 10⁹²(93-digit number)

94678160240971782908…99861236279720408159

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

9.467 × 10⁹²(93-digit number)

94678160240971782908…99861236279720408159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.893 × 10⁹³(94-digit number)

18935632048194356581…99722472559440816319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.787 × 10⁹³(94-digit number)

37871264096388713163…99444945118881632639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.574 × 10⁹³(94-digit number)

75742528192777426326…98889890237763265279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.514 × 10⁹⁴(95-digit number)

15148505638555485265…97779780475526530559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.029 × 10⁹⁴(95-digit number)

30297011277110970530…95559560951053061119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.059 × 10⁹⁴(95-digit number)

60594022554221941061…91119121902106122239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.211 × 10⁹⁵(96-digit number)

12118804510844388212…82238243804212244479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.423 × 10⁹⁵(96-digit number)

24237609021688776424…64476487608424488959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.847 × 10⁹⁵(96-digit number)

48475218043377552848…28952975216848977919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #243,639

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