Block #498,490

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/18/2014, 3:19:13 AM · Difficulty 10.7803 · 6,305,289 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e47b35f2abcd429f2b93d70a24bf78dcffed81743abef0847424b7e59e8c1d2a

View on Chainz ↗

Height

#498,490

Difficulty

10.780315

Transactions

Size

732 B

Version

Bits

0ac7c2b7

Nonce

456,155

Timestamp

4/18/2014, 3:19:13 AM

Confirmations

6,305,289

Mined by

⛏️ :SAeX2hokFQpmApFfNcLFPn3VUNCDqikhfHW

Merkle Root

260b0808d7f6dcf30fef5292996c966ac35abdd5b49938ae0276d284750bd893

Transactions (1)

Coinbase260b0808d7f6dc…76d284750bd893

1 in → 17 out8.5900 XPM641 B

AeX2hokF…DqikhfHW ATp4jJhs…TbSgR8Qb AZcBq6Hw…SpnABb5B AQS6zv5q…6GzKJi4b AdoqUYAy…tJ482T9b

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.

9.071 × 10⁹⁵(96-digit number)

90713118413093336190…30249128287092135479

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

9.071 × 10⁹⁵(96-digit number)

90713118413093336190…30249128287092135479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.814 × 10⁹⁶(97-digit number)

18142623682618667238…60498256574184270959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.628 × 10⁹⁶(97-digit number)

36285247365237334476…20996513148368541919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.257 × 10⁹⁶(97-digit number)

72570494730474668952…41993026296737083839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.451 × 10⁹⁷(98-digit number)

14514098946094933790…83986052593474167679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.902 × 10⁹⁷(98-digit number)

29028197892189867580…67972105186948335359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.805 × 10⁹⁷(98-digit number)

58056395784379735161…35944210373896670719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.161 × 10⁹⁸(99-digit number)

11611279156875947032…71888420747793341439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.322 × 10⁹⁸(99-digit number)

23222558313751894064…43776841495586682879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.644 × 10⁹⁸(99-digit number)

46445116627503788129…87553682991173365759

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