Block #36,430

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/14/2013, 9:23:38 AM · Difficulty 7.9954 · 6,753,303 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6ee4ab154c42da786d1eedfcaf3892cf61a6b6d1949d0b3b205344e185685786

View on Chainz ↗

Height

#36,430

Difficulty

7.995369

Transactions

Size

200 B

Version

Bits

07fed086

Nonce

345

Timestamp

7/14/2013, 9:23:38 AM

Confirmations

6,753,303

Merkle Root

f38a6e2b5da2925fc57c1963d03d878fdc3864559466da390905ddb27cecc682

Transactions (1)

Coinbasef38a6e2b5da292…05ddb27cecc682

1 in → 1 out15.6200 XPM110 B

AbD29oTb…cp9Sovg7

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.

3.834 × 10⁹⁴(95-digit number)

38347138404485714545…34414408593889856139

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

3.834 × 10⁹⁴(95-digit number)

38347138404485714545…34414408593889856139

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.669 × 10⁹⁴(95-digit number)

76694276808971429090…68828817187779712279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.533 × 10⁹⁵(96-digit number)

15338855361794285818…37657634375559424559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.067 × 10⁹⁵(96-digit number)

30677710723588571636…75315268751118849119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.135 × 10⁹⁵(96-digit number)

61355421447177143272…50630537502237698239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.227 × 10⁹⁶(97-digit number)

12271084289435428654…01261075004475396479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.454 × 10⁹⁶(97-digit number)

24542168578870857308…02522150008950792959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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