Block #396,641

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/9/2014, 1:01:46 PM · Difficulty 10.4147 · 6,405,949 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6fd4d8e4badce844a3c42fdb7a1dd786baef246982bd74c531a8a961cb89004d

View on Chainz ↗

Height

#396,641

Difficulty

10.414671

Transactions

Size

938 B

Version

Bits

0a6a27db

Nonce

232,966

Timestamp

2/9/2014, 1:01:46 PM

Confirmations

6,405,949

Mined by

⛏️ aAcgDwGo8ZBUgEksBhbzKTxBsGWBBFwbjVo

Merkle Root

bb51e1c4f4dd051f2b149b20cf847fa0dbeb6d988cce7f316cd98d2673af4d2d

Transactions (1)

Coinbasebb51e1c4f4dd05…d98d2673af4d2d

1 in → 23 out9.2100 XPM845 B

AcgDwGo8…BBFwbjVo AbPcCMg4…719q6mAX Acs9SHrk…QJSB8SFG AZr7Ptuw…CM4Yw5jq ATp4jJhs…TbSgR8Qb

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.

9.680 × 10¹⁰⁰(101-digit number)

96805959113865690322…76687084437067520001

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

9.680 × 10¹⁰⁰(101-digit number)

96805959113865690322…76687084437067520001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.936 × 10¹⁰¹(102-digit number)

19361191822773138064…53374168874135040001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.872 × 10¹⁰¹(102-digit number)

38722383645546276128…06748337748270080001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.744 × 10¹⁰¹(102-digit number)

77444767291092552257…13496675496540160001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.548 × 10¹⁰²(103-digit number)

15488953458218510451…26993350993080320001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.097 × 10¹⁰²(103-digit number)

30977906916437020903…53986701986160640001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.195 × 10¹⁰²(103-digit number)

61955813832874041806…07973403972321280001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.239 × 10¹⁰³(104-digit number)

12391162766574808361…15946807944642560001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.478 × 10¹⁰³(104-digit number)

24782325533149616722…31893615889285120001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.956 × 10¹⁰³(104-digit number)

49564651066299233445…63787231778570240001

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