Block #406,778

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/16/2014, 12:00:30 PM · Difficulty 10.4325 · 6,394,776 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

46d30d4e5599cd23d1e0fe08e2ffc99aad094baf57337769f90349c7e44237ac

View on Chainz ↗

Height

#406,778

Difficulty

10.432522

Transactions

Size

868 B

Version

Bits

0a6eb9bf

Nonce

116,003

Timestamp

2/16/2014, 12:00:30 PM

Confirmations

6,394,776

Mined by

⛏️ 4aSNAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2005c62189a5823152592c5128de7038993ad2a70531ba36b58937ed08e36588

Transactions (1)

Coinbase2005c62189a582…8937ed08e36588

1 in → 21 out9.1700 XPM777 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 ALqxX1WA…hsKjbnXn ATKK7iFz…wZm46KN1

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.

2.736 × 10⁹⁶(97-digit number)

27361838807884987586…12098118798268034241

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

2.736 × 10⁹⁶(97-digit number)

27361838807884987586…12098118798268034241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.472 × 10⁹⁶(97-digit number)

54723677615769975173…24196237596536068481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.094 × 10⁹⁷(98-digit number)

10944735523153995034…48392475193072136961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.188 × 10⁹⁷(98-digit number)

21889471046307990069…96784950386144273921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.377 × 10⁹⁷(98-digit number)

43778942092615980138…93569900772288547841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.755 × 10⁹⁷(98-digit number)

87557884185231960277…87139801544577095681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.751 × 10⁹⁸(99-digit number)

17511576837046392055…74279603089154191361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.502 × 10⁹⁸(99-digit number)

35023153674092784111…48559206178308382721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.004 × 10⁹⁸(99-digit number)

70046307348185568222…97118412356616765441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.400 × 10⁹⁹(100-digit number)

14009261469637113644…94236824713233530881

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