Block #296,406

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 12/6/2013, 12:05:39 AM · Difficulty 9.9917 · 6,511,446 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b7b7227c70f7cc28c7e363c9814c7d13aed1aaa9160cf8bd4bc1b8651a16b72d

View on Chainz ↗

Height

#296,406

Difficulty

9.991700

Transactions

Size

1.01 KB

Version

Bits

09fde009

Nonce

255,368

Timestamp

12/6/2013, 12:05:39 AM

Confirmations

6,511,446

Mined by

⛏️ aRAZMdkwZ886CNQf3beKnnFxmDJyxgjWF8DU

Merkle Root

cd3ed1ba00cdc5c05b25bb0299536534ebe8c3f7233efb0685477abc44606c4c

Transactions (1)

Coinbasecd3ed1ba00cdc5…477abc44606c4c

1 in → 26 out10.0000 XPM947 B

AZMdkwZ8…xgjWF8DU AYPb2Rez…ReMAwnVN AHqZtsfn…WrCGjM3J AXX2MCBh…Q97G5hHt AUFxANzC…wSxXZx69

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.

4.554 × 10⁹⁰(91-digit number)

45547674196031420040…50156628665895518719

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

4.554 × 10⁹⁰(91-digit number)

45547674196031420040…50156628665895518719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.109 × 10⁹⁰(91-digit number)

91095348392062840080…00313257331791037439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.821 × 10⁹¹(92-digit number)

18219069678412568016…00626514663582074879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.643 × 10⁹¹(92-digit number)

36438139356825136032…01253029327164149759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.287 × 10⁹¹(92-digit number)

72876278713650272064…02506058654328299519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.457 × 10⁹²(93-digit number)

14575255742730054412…05012117308656599039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.915 × 10⁹²(93-digit number)

29150511485460108825…10024234617313198079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.830 × 10⁹²(93-digit number)

58301022970920217651…20048469234626396159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.166 × 10⁹³(94-digit number)

11660204594184043530…40096938469252792319

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

Block #296,406

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