Block #75,541

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/21/2013, 5:05:07 PM · Difficulty 9.0151 · 6,714,397 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6ee4e49dcc95a2373ffd4c34dc1e6471626d60d59dace800c1a45aa966d61802

View on Chainz ↗

Height

#75,541

Difficulty

9.015076

Transactions

Size

201 B

Version

Bits

0903dbff

Nonce

108

Timestamp

7/21/2013, 5:05:07 PM

Confirmations

6,714,397

Merkle Root

86050435dadca6f6c1ad2c07f7ecbf2dd6779b0e142549fa6b2f880ec1798cce

Transactions (1)

Coinbase86050435dadca6…2f880ec1798cce

1 in → 1 out12.2900 XPM110 B

AK1JUKWL…oPR4rN5o

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.

2.766 × 10⁹⁷(98-digit number)

27661350254087900462…59400883772464277249

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

2.766 × 10⁹⁷(98-digit number)

27661350254087900462…59400883772464277249

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.532 × 10⁹⁷(98-digit number)

55322700508175800925…18801767544928554499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.106 × 10⁹⁸(99-digit number)

11064540101635160185…37603535089857108999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.212 × 10⁹⁸(99-digit number)

22129080203270320370…75207070179714217999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.425 × 10⁹⁸(99-digit number)

44258160406540640740…50414140359428435999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.851 × 10⁹⁸(99-digit number)

88516320813081281480…00828280718856871999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.770 × 10⁹⁹(100-digit number)

17703264162616256296…01656561437713743999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.540 × 10⁹⁹(100-digit number)

35406528325232512592…03313122875427487999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.081 × 10⁹⁹(100-digit number)

70813056650465025184…06626245750854975999

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