Block #408,645

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/17/2014, 7:39:13 PM · Difficulty 10.4300 · 6,397,462 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

abecea4f73475f47f37d13ecbe8069f789b47cf66c285db811b081e8451974a8

View on Chainz ↗

Height

#408,645

Difficulty

10.430021

Transactions

Size

936 B

Version

Bits

0a6e15de

Nonce

819,616

Timestamp

2/17/2014, 7:39:13 PM

Confirmations

6,397,462

Mined by

⛏️ E<aSdlAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

dd018256c0619e38e605455dbfaf243b6b2fdde8250149ad46d6f146cf5dcd2b

Transactions (1)

Coinbasedd018256c0619e…d6f146cf5dcd2b

1 in → 23 out9.1800 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AUnkFe8H…fvenjA4X AN6KvTCW…8tVTJUpq

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.

9.655 × 10⁹⁵(96-digit number)

96557878841969053315…22503319407349535251

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

9.655 × 10⁹⁵(96-digit number)

96557878841969053315…22503319407349535251

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.931 × 10⁹⁶(97-digit number)

19311575768393810663…45006638814699070501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.862 × 10⁹⁶(97-digit number)

38623151536787621326…90013277629398141001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.724 × 10⁹⁶(97-digit number)

77246303073575242652…80026555258796282001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.544 × 10⁹⁷(98-digit number)

15449260614715048530…60053110517592564001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.089 × 10⁹⁷(98-digit number)

30898521229430097060…20106221035185128001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.179 × 10⁹⁷(98-digit number)

61797042458860194121…40212442070370256001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.235 × 10⁹⁸(99-digit number)

12359408491772038824…80424884140740512001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.471 × 10⁹⁸(99-digit number)

24718816983544077648…60849768281481024001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.943 × 10⁹⁸(99-digit number)

49437633967088155297…21699536562962048001

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