Block #275,672

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/26/2013, 7:49:31 PM · Difficulty 9.9613 · 6,535,432 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

82b88696208542b48f817ac1e667e90ce1c99ec58cf604227d6086b44115e2af

View on Chainz ↗

Height

#275,672

Difficulty

9.961331

Transactions

Size

1.01 KB

Version

Bits

09f619d0

Nonce

15,739

Timestamp

11/26/2013, 7:49:31 PM

Confirmations

6,535,432

Mined by

⛏️ 4aRBAVss9H5FkXhhqqTXyhqhrXDK3UzXhyMijY

Merkle Root

10926fb7d6f876a1af9dbd53578727620c184b2db48adbc6419df78f73f2140c

Transactions (1)

Coinbase10926fb7d6f876…9df78f73f2140c

1 in → 26 out10.0600 XPM947 B

AVss9H5F…zXhyMijY Ac5sZcdP…kzV4eckG AWA5FEzr…x9RdPKTy ALjKzW6p…eTWrinY7 AN63YyQR…1tfe566A

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.

2.488 × 10⁹⁷(98-digit number)

24885053801168440189…77010310371543134719

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

2.488 × 10⁹⁷(98-digit number)

24885053801168440189…77010310371543134719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.977 × 10⁹⁷(98-digit number)

49770107602336880378…54020620743086269439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.954 × 10⁹⁷(98-digit number)

99540215204673760756…08041241486172538879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.990 × 10⁹⁸(99-digit number)

19908043040934752151…16082482972345077759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.981 × 10⁹⁸(99-digit number)

39816086081869504302…32164965944690155519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.963 × 10⁹⁸(99-digit number)

79632172163739008604…64329931889380311039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.592 × 10⁹⁹(100-digit number)

15926434432747801720…28659863778760622079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.185 × 10⁹⁹(100-digit number)

31852868865495603441…57319727557521244159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.370 × 10⁹⁹(100-digit number)

63705737730991206883…14639455115042488319

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 #275,672

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