Block #136,044

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/26/2013, 11:50:29 PM · Difficulty 9.8139 · 6,653,681 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c22d288c93f289cb94ebcb200b8079d16e936bc8bf117f3239504feeee36640b

View on Chainz ↗

Height

#136,044

Difficulty

9.813914

Transactions

Size

197 B

Version

Bits

09d05ca9

Nonce

3,018

Timestamp

8/26/2013, 11:50:29 PM

Confirmations

6,653,681

Merkle Root

c84fa4d7262dad68bc316836b31072cedc17588fc94910d1ea81780ad06402cd

Transactions (1)

Coinbasec84fa4d7262dad…81780ad06402cd

1 in → 1 out10.3700 XPM109 B

AKvyBU9y…fsbF4gSc

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.

5.202 × 10⁸⁸(89-digit number)

52028498700876451851…08789643114826914499

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

5.202 × 10⁸⁸(89-digit number)

52028498700876451851…08789643114826914499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.040 × 10⁸⁹(90-digit number)

10405699740175290370…17579286229653828999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.081 × 10⁸⁹(90-digit number)

20811399480350580740…35158572459307657999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.162 × 10⁸⁹(90-digit number)

41622798960701161480…70317144918615315999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.324 × 10⁸⁹(90-digit number)

83245597921402322961…40634289837230631999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.664 × 10⁹⁰(91-digit number)

16649119584280464592…81268579674461263999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.329 × 10⁹⁰(91-digit number)

33298239168560929184…62537159348922527999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.659 × 10⁹⁰(91-digit number)

66596478337121858369…25074318697845055999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.331 × 10⁹¹(92-digit number)

13319295667424371673…50148637395690111999

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