Block #399,447

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/11/2014, 10:36:14 AM · Difficulty 10.4238 · 6,392,360 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

398465b290e8860f3ebc24c13462c9961aa135225e31ad2264b009df22026118

View on Chainz ↗

Height

#399,447

Difficulty

10.423839

Transactions

Size

862 B

Version

Bits

0a6c80b4

Nonce

235,594

Timestamp

2/11/2014, 10:36:14 AM

Confirmations

6,392,360

Merkle Root

0c21a3e075df61105a52ce1705a08d565f110667811f291314384cde3ab352f7

Transactions (2)

Coinbase54aafa081ad9f0…ead5f878a39928

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

9ecf66547eaea4…d1dec025590771

3 in → 9 out27.6200 XPM655 B

AbzaNX1N…AY2wAuNd AQYQT37a…woJiw19q AZZSguRi…GvQsves1 ARJQsNEx…UvYvuSPW AXHFnvkB…yXdZX2Fh

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.

1.242 × 10⁹⁸(99-digit number)

12422412456244929337…22165656976611341189

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

1.242 × 10⁹⁸(99-digit number)

12422412456244929337…22165656976611341189

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.484 × 10⁹⁸(99-digit number)

24844824912489858674…44331313953222682379

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.968 × 10⁹⁸(99-digit number)

49689649824979717349…88662627906445364759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.937 × 10⁹⁸(99-digit number)

99379299649959434699…77325255812890729519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.987 × 10⁹⁹(100-digit number)

19875859929991886939…54650511625781459039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.975 × 10⁹⁹(100-digit number)

39751719859983773879…09301023251562918079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.950 × 10⁹⁹(100-digit number)

79503439719967547759…18602046503125836159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.590 × 10¹⁰⁰(101-digit number)

15900687943993509551…37204093006251672319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.180 × 10¹⁰⁰(101-digit number)

31801375887987019103…74408186012503344639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.360 × 10¹⁰⁰(101-digit number)

63602751775974038207…48816372025006689279

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