Block #489,396

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/13/2014, 6:37:36 AM · Difficulty 10.6649 · 6,305,901 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7e86bdd91414c1230e638d5fbc015a2ff89322ce9cb66d135832e9dbb2e1d6e7

View on Chainz ↗

Height

#489,396

Difficulty

10.664937

Transactions

Size

799 B

Version

Bits

0aaa3948

Nonce

24,794

Timestamp

4/13/2014, 6:37:36 AM

Confirmations

6,305,901

Mined by

⛏️ waSJ0DAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

dcc89caa4dabe8aff11da655f7ac5854a047e4de11656fd7dc0daa01ffa43e36

Transactions (1)

Coinbasedcc89caa4dabe8…0daa01ffa43e36

1 in → 19 out8.7800 XPM708 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 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.

5.117 × 10⁹⁶(97-digit number)

51177273004841438611…93236781745274416001

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

5.117 × 10⁹⁶(97-digit number)

51177273004841438611…93236781745274416001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.023 × 10⁹⁷(98-digit number)

10235454600968287722…86473563490548832001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.047 × 10⁹⁷(98-digit number)

20470909201936575444…72947126981097664001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.094 × 10⁹⁷(98-digit number)

40941818403873150889…45894253962195328001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.188 × 10⁹⁷(98-digit number)

81883636807746301778…91788507924390656001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.637 × 10⁹⁸(99-digit number)

16376727361549260355…83577015848781312001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.275 × 10⁹⁸(99-digit number)

32753454723098520711…67154031697562624001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.550 × 10⁹⁸(99-digit number)

65506909446197041422…34308063395125248001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.310 × 10⁹⁹(100-digit number)

13101381889239408284…68616126790250496001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.620 × 10⁹⁹(100-digit number)

26202763778478816569…37232253580500992001

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer