Block #389,379

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2014, 11:11:39 AM · Difficulty 10.4185 · 6,413,317 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

63dfad8f6e21e8fe0094d0448d83bc49b96e5ee2fd83ecf413af02a222023426

View on Chainz ↗

Height

#389,379

Difficulty

10.418530

Transactions

Size

870 B

Version

Bits

0a6b24c5

Nonce

74,240

Timestamp

2/4/2014, 11:11:39 AM

Confirmations

6,413,317

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1749c1be31f4c18f12d324c74e737927f6f3b8db215a5bcfea8de10a8dbba719

Transactions (1)

Coinbase1749c1be31f4c1…8de10a8dbba719

1 in → 21 out9.2000 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6 AFutDVqJ…TJTJj6UF

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.

6.326 × 10¹⁰⁰(101-digit number)

63261415511522903849…95876304591525570561

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

6.326 × 10¹⁰⁰(101-digit number)

63261415511522903849…95876304591525570561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.265 × 10¹⁰¹(102-digit number)

12652283102304580769…91752609183051141121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.530 × 10¹⁰¹(102-digit number)

25304566204609161539…83505218366102282241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.060 × 10¹⁰¹(102-digit number)

50609132409218323079…67010436732204564481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.012 × 10¹⁰²(103-digit number)

10121826481843664615…34020873464409128961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.024 × 10¹⁰²(103-digit number)

20243652963687329231…68041746928818257921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.048 × 10¹⁰²(103-digit number)

40487305927374658463…36083493857636515841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.097 × 10¹⁰²(103-digit number)

80974611854749316927…72166987715273031681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.619 × 10¹⁰³(104-digit number)

16194922370949863385…44333975430546063361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.238 × 10¹⁰³(104-digit number)

32389844741899726770…88667950861092126721

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