Block #531,426

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/8/2014, 12:09:29 PM · Difficulty 10.8941 · 6,262,928 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a8bcad74ef8137ee8c2bdbd2ebf9f39397621de40deee4bff01765222469b41f

View on Chainz ↗

Height

#531,426

Difficulty

10.894095

Transactions

Size

434 B

Version

Bits

0ae4e369

Nonce

183,008

Timestamp

5/8/2014, 12:09:29 PM

Confirmations

6,262,928

Merkle Root

d39c97a17da5045f2d8faedde081441968495639b633ff08cc738b9314cb70aa

Transactions (2)

Coinbaseef2d2bd729d267…8e64fa0f72fde1

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

ebf518265b5691…e429a41f853cf2

1 in → 2 out6.3789 XPM226 B

AWqJRFnX…smM7AuX3 AYtDHKWG…MSKYtrsp

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.

6.395 × 10⁹⁹(100-digit number)

63956840189438999482…53684845951267378241

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

6.395 × 10⁹⁹(100-digit number)

63956840189438999482…53684845951267378241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.279 × 10¹⁰⁰(101-digit number)

12791368037887799896…07369691902534756481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.558 × 10¹⁰⁰(101-digit number)

25582736075775599793…14739383805069512961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.116 × 10¹⁰⁰(101-digit number)

51165472151551199586…29478767610139025921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.023 × 10¹⁰¹(102-digit number)

10233094430310239917…58957535220278051841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.046 × 10¹⁰¹(102-digit number)

20466188860620479834…17915070440556103681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.093 × 10¹⁰¹(102-digit number)

40932377721240959669…35830140881112207361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.186 × 10¹⁰¹(102-digit number)

81864755442481919338…71660281762224414721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.637 × 10¹⁰²(103-digit number)

16372951088496383867…43320563524448829441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.274 × 10¹⁰²(103-digit number)

32745902176992767735…86641127048897658881

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