Block #279,698

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/28/2013, 10:37:55 AM · Difficulty 9.9725 · 6,512,015 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0e5e8afe28a4542bce694af4524f593154783453104c6b8cdc3cf91b2d5c132d

View on Chainz ↗

Height

#279,698

Difficulty

9.972516

Transactions

Size

205 B

Version

Bits

09f8f6d0

Nonce

78,954

Timestamp

11/28/2013, 10:37:55 AM

Confirmations

6,512,015

Merkle Root

ce6fd482e6f13c51c0a9990d7d1dabd0dd9eaca5e1a64d24dbc2c48762a11fb4

Transactions (1)

Coinbasece6fd482e6f13c…c2c48762a11fb4

1 in → 1 out10.0400 XPM116 B

AcLBm5Z9…S683d7c3

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.

3.501 × 10⁹²(93-digit number)

35019856168378136142…84961978248352635199

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

3.501 × 10⁹²(93-digit number)

35019856168378136142…84961978248352635199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.003 × 10⁹²(93-digit number)

70039712336756272285…69923956496705270399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.400 × 10⁹³(94-digit number)

14007942467351254457…39847912993410540799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.801 × 10⁹³(94-digit number)

28015884934702508914…79695825986821081599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.603 × 10⁹³(94-digit number)

56031769869405017828…59391651973642163199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.120 × 10⁹⁴(95-digit number)

11206353973881003565…18783303947284326399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.241 × 10⁹⁴(95-digit number)

22412707947762007131…37566607894568652799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.482 × 10⁹⁴(95-digit number)

44825415895524014262…75133215789137305599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.965 × 10⁹⁴(95-digit number)

89650831791048028525…50266431578274611199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.793 × 10⁹⁵(96-digit number)

17930166358209605705…00532863156549222399

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