Block #279,581

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/28/2013, 9:42:05 AM · Difficulty 9.9722 · 6,512,882 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d65624860eb4689e738658880e19a483e2befb966a7a07bda10ac4d66800879e

View on Chainz ↗

Height

#279,581

Difficulty

9.972171

Transactions

Size

813 B

Version

Bits

09f8e02b

Nonce

33,250

Timestamp

11/28/2013, 9:42:05 AM

Confirmations

6,512,882

Merkle Root

8a785a64ca9d9b79176c65870d1f6182dd91924653a36673801fb5d3c581d065

Transactions (2)

Coinbase43885f80a060e9…8839182fca0a2b

1 in → 1 out10.0500 XPM110 B

AeKNrjNj…1NEq95Ta

2cdea9d3af03bd…9dd71cafe3a3a8

5 in → 1 out50.4200 XPM614 B

AS4NDvjA…WVL9Cvd1

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.

2.087 × 10⁹³(94-digit number)

20870674749108197163…17178684315216666559

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

2.087 × 10⁹³(94-digit number)

20870674749108197163…17178684315216666559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.174 × 10⁹³(94-digit number)

41741349498216394326…34357368630433333119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.348 × 10⁹³(94-digit number)

83482698996432788653…68714737260866666239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.669 × 10⁹⁴(95-digit number)

16696539799286557730…37429474521733332479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.339 × 10⁹⁴(95-digit number)

33393079598573115461…74858949043466664959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.678 × 10⁹⁴(95-digit number)

66786159197146230922…49717898086933329919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.335 × 10⁹⁵(96-digit number)

13357231839429246184…99435796173866659839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.671 × 10⁹⁵(96-digit number)

26714463678858492369…98871592347733319679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.342 × 10⁹⁵(96-digit number)

53428927357716984738…97743184695466639359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.068 × 10⁹⁶(97-digit number)

10685785471543396947…95486369390933278719

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