Block #457,165

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/23/2014, 5:07:41 PM · Difficulty 10.4213 · 6,338,826 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

019de1129daca22435c930423d9839e8ef0472df7d35532db39aad14e4fdcaa6

View on Chainz ↗

Height

#457,165

Difficulty

10.421313

Transactions

Size

868 B

Version

Bits

0a6bdb2a

Nonce

18,992

Timestamp

3/23/2014, 5:07:41 PM

Confirmations

6,338,826

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

9df0980f966ff16705298a8a87db34ec0551de2f2837b9c61d1828c9c736ceb7

Transactions (1)

Coinbase9df0980f966ff1…1828c9c736ceb7

1 in → 21 out9.1900 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AUDD9tmA…gJPQLnsz AUFKXvnz…342ApNcm AH5mD99t…Spv1yg4N

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.

1.904 × 10⁹⁷(98-digit number)

19046331459757769745…68486370443653488639

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

1.904 × 10⁹⁷(98-digit number)

19046331459757769745…68486370443653488639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.809 × 10⁹⁷(98-digit number)

38092662919515539490…36972740887306977279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.618 × 10⁹⁷(98-digit number)

76185325839031078981…73945481774613954559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.523 × 10⁹⁸(99-digit number)

15237065167806215796…47890963549227909119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.047 × 10⁹⁸(99-digit number)

30474130335612431592…95781927098455818239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.094 × 10⁹⁸(99-digit number)

60948260671224863184…91563854196911636479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.218 × 10⁹⁹(100-digit number)

12189652134244972636…83127708393823272959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.437 × 10⁹⁹(100-digit number)

24379304268489945273…66255416787646545919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.875 × 10⁹⁹(100-digit number)

48758608536979890547…32510833575293091839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.751 × 10⁹⁹(100-digit number)

97517217073959781095…65021667150586183679

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