Block #375,420

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/25/2014, 4:59:00 PM · Difficulty 10.4246 · 6,427,190 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2d300fa3becc08e9b594a082bb97821172391127b7f54f0eb2b466d0c6c19a22

View on Chainz ↗

Height

#375,420

Difficulty

10.424642

Transactions

Size

832 B

Version

Bits

0a6cb55a

Nonce

464,347

Timestamp

1/25/2014, 4:59:00 PM

Confirmations

6,427,190

Mined by

⛏️ |aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

dc435df0ca415fac874939f8d42f77067e54428a34eeb9d85de1d584ece08fed

Transactions (1)

Coinbasedc435df0ca415f…e1d584ece08fed

1 in → 20 out9.1900 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

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.

6.034 × 10⁹²(93-digit number)

60340766199653465725…97431713733768038399

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

6.034 × 10⁹²(93-digit number)

60340766199653465725…97431713733768038399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.206 × 10⁹³(94-digit number)

12068153239930693145…94863427467536076799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.413 × 10⁹³(94-digit number)

24136306479861386290…89726854935072153599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.827 × 10⁹³(94-digit number)

48272612959722772580…79453709870144307199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.654 × 10⁹³(94-digit number)

96545225919445545161…58907419740288614399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.930 × 10⁹⁴(95-digit number)

19309045183889109032…17814839480577228799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.861 × 10⁹⁴(95-digit number)

38618090367778218064…35629678961154457599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.723 × 10⁹⁴(95-digit number)

77236180735556436129…71259357922308915199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.544 × 10⁹⁵(96-digit number)

15447236147111287225…42518715844617830399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.089 × 10⁹⁵(96-digit number)

30894472294222574451…85037431689235660799

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