Block #447,816

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/17/2014, 12:36:01 PM · Difficulty 10.3625 · 6,355,541 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f21f10fe0caafeeb3c3b4e55e7b68393217948171800c5f811e4b2f53b5c5303

View on Chainz ↗

Height

#447,816

Difficulty

10.362463

Transactions

Size

1.28 KB

Version

Bits

0a5cca60

Nonce

247,212

Timestamp

3/17/2014, 12:36:01 PM

Confirmations

6,355,541

Mined by

⛏️ HaS&AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

6dc6e59f424922775b409bdce14c63f7821f2f2031f371eacc7122d0f4c41294

Transactions (2)

Coinbase3aed2ac3f06d29…825263c77416bf

1 in → 23 out9.3000 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 AdhWfaX2…aX7YvEJq

c61e7b7d10eac8…931f5371008d59

2 in → 2 out2.5949 XPM374 B

AbWLE1Ys…RjBwdV5u AdAFFs23…5xsNKSP8

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.

1.756 × 10⁹³(94-digit number)

17563799734605397731…97943280222087382159

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

1.756 × 10⁹³(94-digit number)

17563799734605397731…97943280222087382159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.512 × 10⁹³(94-digit number)

35127599469210795462…95886560444174764319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.025 × 10⁹³(94-digit number)

70255198938421590924…91773120888349528639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.405 × 10⁹⁴(95-digit number)

14051039787684318184…83546241776699057279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.810 × 10⁹⁴(95-digit number)

28102079575368636369…67092483553398114559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.620 × 10⁹⁴(95-digit number)

56204159150737272739…34184967106796229119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.124 × 10⁹⁵(96-digit number)

11240831830147454547…68369934213592458239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.248 × 10⁹⁵(96-digit number)

22481663660294909095…36739868427184916479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.496 × 10⁹⁵(96-digit number)

44963327320589818191…73479736854369832959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.992 × 10⁹⁵(96-digit number)

89926654641179636382…46959473708739665919

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