Block #278,261

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 10:04:30 PM · Difficulty 9.9685 · 6,513,157 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

00967e2960f4942ae105333a834312463521718fe8e216a178568280df8f8d57

View on Chainz ↗

Height

#278,261

Difficulty

9.968471

Transactions

Size

1.08 KB

Version

Bits

09f7edbb

Nonce

5,522

Timestamp

11/27/2013, 10:04:30 PM

Confirmations

6,513,157

Merkle Root

7966b2cdf488e03f184543754040d2ab7ebc5f2cd3adcacd3dba64a0e1f91e7a

Transactions (1)

Coinbase7966b2cdf488e0…ba64a0e1f91e7a

1 in → 28 out10.0300 XPM1015 B

AaBbvGyk…q1UtX4iZ Aai6TNLM…kQf2QbQd ALw8WzMm…sj2uYfgL AbiApRgN…g8QuFUwL AGt31xEv…GewYq26v

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.

3.258 × 10⁹²(93-digit number)

32587560308568827722…89858913952670908799

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

3.258 × 10⁹²(93-digit number)

32587560308568827722…89858913952670908799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.517 × 10⁹²(93-digit number)

65175120617137655444…79717827905341817599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.303 × 10⁹³(94-digit number)

13035024123427531088…59435655810683635199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.607 × 10⁹³(94-digit number)

26070048246855062177…18871311621367270399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.214 × 10⁹³(94-digit number)

52140096493710124355…37742623242734540799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.042 × 10⁹⁴(95-digit number)

10428019298742024871…75485246485469081599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.085 × 10⁹⁴(95-digit number)

20856038597484049742…50970492970938163199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.171 × 10⁹⁴(95-digit number)

41712077194968099484…01940985941876326399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.342 × 10⁹⁴(95-digit number)

83424154389936198968…03881971883752652799

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