Block #438,616

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/11/2014, 3:30:21 AM · Difficulty 10.3556 · 6,355,750 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f6a4527a76066fdf063a9cb81c9ddd80c7b98df7aa91a87d0aad0bffb2b525ee

View on Chainz ↗

Height

#438,616

Difficulty

10.355641

Transactions

Size

539 B

Version

Bits

0a5b0b4e

Nonce

164,463

Timestamp

3/11/2014, 3:30:21 AM

Confirmations

6,355,750

Merkle Root

a2e71587515a7710b206af216c9f49b8c548d63d83ddf435ef905127e53719f1

Transactions (2)

Coinbasef8489184ab79a1…e1867376015801

1 in → 1 out9.3200 XPM109 B

AW58rHF6…qv88wuKW

3c98830d729897…7cf314ff77e6e6

2 in → 1 out158.9000 XPM341 B

AFrSi5NH…MSYsDScf

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.

3.195 × 10⁹³(94-digit number)

31955027340090357634…63885398604652441549

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

3.195 × 10⁹³(94-digit number)

31955027340090357634…63885398604652441549

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.391 × 10⁹³(94-digit number)

63910054680180715269…27770797209304883099

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.278 × 10⁹⁴(95-digit number)

12782010936036143053…55541594418609766199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.556 × 10⁹⁴(95-digit number)

25564021872072286107…11083188837219532399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.112 × 10⁹⁴(95-digit number)

51128043744144572215…22166377674439064799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.022 × 10⁹⁵(96-digit number)

10225608748828914443…44332755348878129599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.045 × 10⁹⁵(96-digit number)

20451217497657828886…88665510697756259199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.090 × 10⁹⁵(96-digit number)

40902434995315657772…77331021395512518399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.180 × 10⁹⁵(96-digit number)

81804869990631315544…54662042791025036799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.636 × 10⁹⁶(97-digit number)

16360973998126263108…09324085582050073599

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