Block #495,828

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/16/2014, 7:17:01 PM · Difficulty 10.7451 · 6,295,999 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

24258f17130298a502d2dad82b53a467c60133fc644e162cf1f207dfe323f5f2

View on Chainz ↗

Height

#495,828

Difficulty

10.745102

Transactions

Size

936 B

Version

Bits

0abebeff

Nonce

79,231

Timestamp

4/16/2014, 7:17:01 PM

Confirmations

6,295,999

Merkle Root

6907b164751c0b9245b137ce0a6ee5dfcfa6dd9280fd30111dce0ce051afc712

Transactions (1)

Coinbase6907b164751c0b…ce0ce051afc712

1 in → 23 out8.6500 XPM845 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AMdvB6BS…DPq9FYdA AScAzqGc…BZ6tV1vJ

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.

1.043 × 10⁹⁸(99-digit number)

10439886174591355497…14228397215213016319

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

1.043 × 10⁹⁸(99-digit number)

10439886174591355497…14228397215213016319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.087 × 10⁹⁸(99-digit number)

20879772349182710994…28456794430426032639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.175 × 10⁹⁸(99-digit number)

41759544698365421988…56913588860852065279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.351 × 10⁹⁸(99-digit number)

83519089396730843977…13827177721704130559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.670 × 10⁹⁹(100-digit number)

16703817879346168795…27654355443408261119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.340 × 10⁹⁹(100-digit number)

33407635758692337591…55308710886816522239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.681 × 10⁹⁹(100-digit number)

66815271517384675182…10617421773633044479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.336 × 10¹⁰⁰(101-digit number)

13363054303476935036…21234843547266088959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.672 × 10¹⁰⁰(101-digit number)

26726108606953870072…42469687094532177919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.345 × 10¹⁰⁰(101-digit number)

53452217213907740145…84939374189064355839

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