Block #495,708

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/16/2014, 6:11:21 PM · Difficulty 10.7423 · 6,308,071 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

14f52980888a7a36d3921c3ed1908210c292ba0f056a52db14f10b19008816df

View on Chainz ↗

Height

#495,708

Difficulty

10.742302

Transactions

Size

901 B

Version

Bits

0abe0781

Nonce

6,756

Timestamp

4/16/2014, 6:11:21 PM

Confirmations

6,308,071

Mined by

⛏️ \aSNAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

24c789cbb95b3e40b3fa57c7da7babaab47c1f5f00be10c089f9c771a6f41a9b

Transactions (1)

Coinbase24c789cbb95b3e…f9c771a6f41a9b

1 in → 22 out8.6500 XPM811 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AWMrD5hP…ZwsoxvZ3

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.

7.291 × 10⁹³(94-digit number)

72919835548802373736…32559444304674038199

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

7.291 × 10⁹³(94-digit number)

72919835548802373736…32559444304674038199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.458 × 10⁹⁴(95-digit number)

14583967109760474747…65118888609348076399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.916 × 10⁹⁴(95-digit number)

29167934219520949494…30237777218696152799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.833 × 10⁹⁴(95-digit number)

58335868439041898988…60475554437392305599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.166 × 10⁹⁵(96-digit number)

11667173687808379797…20951108874784611199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.333 × 10⁹⁵(96-digit number)

23334347375616759595…41902217749569222399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.666 × 10⁹⁵(96-digit number)

46668694751233519191…83804435499138444799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.333 × 10⁹⁵(96-digit number)

93337389502467038382…67608870998276889599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.866 × 10⁹⁶(97-digit number)

18667477900493407676…35217741996553779199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.733 × 10⁹⁶(97-digit number)

37334955800986815352…70435483993107558399

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