Block #449,181

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/18/2014, 10:41:44 AM · Difficulty 10.3683 · 6,359,283 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2d58538dc805938897f6c209fe316ba6f1d1f55cfe313dd7e9ade18a212e210d

View on Chainz ↗

Height

#449,181

Difficulty

10.368307

Transactions

Size

970 B

Version

Bits

0a5e495a

Nonce

21,631

Timestamp

3/18/2014, 10:41:44 AM

Confirmations

6,359,283

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

06e9a70713311cbabdfcf85ec927204394133d071f8095d69dea59b63b4323eb

Transactions (1)

Coinbase06e9a70713311c…ea59b63b4323eb

1 in → 24 out9.2850 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

7.564 × 10⁹⁵(96-digit number)

75644125286978192882…71910803394552670959

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

7.564 × 10⁹⁵(96-digit number)

75644125286978192882…71910803394552670959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.512 × 10⁹⁶(97-digit number)

15128825057395638576…43821606789105341919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.025 × 10⁹⁶(97-digit number)

30257650114791277152…87643213578210683839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.051 × 10⁹⁶(97-digit number)

60515300229582554305…75286427156421367679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.210 × 10⁹⁷(98-digit number)

12103060045916510861…50572854312842735359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.420 × 10⁹⁷(98-digit number)

24206120091833021722…01145708625685470719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.841 × 10⁹⁷(98-digit number)

48412240183666043444…02291417251370941439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.682 × 10⁹⁷(98-digit number)

96824480367332086889…04582834502741882879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.936 × 10⁹⁸(99-digit number)

19364896073466417377…09165669005483765759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.872 × 10⁹⁸(99-digit number)

38729792146932834755…18331338010967531519

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

Block #449,181

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