Block #344,045

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/5/2014, 1:25:27 AM · Difficulty 10.1896 · 6,454,979 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ed4f1398ad6c8771577a58453ff7c5234721579b87fe3a9a9a5f498f46704e73

View on Chainz ↗

Height

#344,045

Difficulty

10.189574

Transactions

Size

1.01 KB

Version

Bits

0a3087ec

Nonce

64,856

Timestamp

1/5/2014, 1:25:27 AM

Confirmations

6,454,979

Mined by

⛏️ ?aRAZemWJAowt1PBaxKypgqLxhXgv6jhDtieG

Merkle Root

745859f882b58d854772bb7ecebe7c4d25851bba05c7f3edc4e62a5080523100

Transactions (1)

Coinbase745859f882b58d…e62a5080523100

1 in → 26 out9.6200 XPM947 B

AZemWJAo…6jhDtieG AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR AcuM7XiJ…5uND8Jce Ad9pSzHt…cpJ3y2zz

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.

1.933 × 10¹⁰⁰(101-digit number)

19335060212488435994…08192614935070899199

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

1.933 × 10¹⁰⁰(101-digit number)

19335060212488435994…08192614935070899199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.867 × 10¹⁰⁰(101-digit number)

38670120424976871988…16385229870141798399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.734 × 10¹⁰⁰(101-digit number)

77340240849953743976…32770459740283596799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.546 × 10¹⁰¹(102-digit number)

15468048169990748795…65540919480567193599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.093 × 10¹⁰¹(102-digit number)

30936096339981497590…31081838961134387199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.187 × 10¹⁰¹(102-digit number)

61872192679962995180…62163677922268774399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.237 × 10¹⁰²(103-digit number)

12374438535992599036…24327355844537548799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.474 × 10¹⁰²(103-digit number)

24748877071985198072…48654711689075097599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.949 × 10¹⁰²(103-digit number)

49497754143970396144…97309423378150195199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.899 × 10¹⁰²(103-digit number)

98995508287940792289…94618846756300390399

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