Block #362,346

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/16/2014, 3:54:14 PM · Difficulty 10.4142 · 6,443,616 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

23394604ef7a9ff34f776910fdac2382f4915c84ff75cd4e98818f09f2798a4b

View on Chainz ↗

Height

#362,346

Difficulty

10.414159

Transactions

Size

1.01 KB

Version

Bits

0a6a0653

Nonce

147,847

Timestamp

1/16/2014, 3:54:14 PM

Confirmations

6,443,616

Mined by

⛏️ jaRaAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

20981bf0146906299e95a1d2bdce2602c7793b48b27ebe7df662a57f5cf0bde0

Transactions (1)

Coinbase20981bf0146906…62a57f5cf0bde0

1 in → 26 out9.2100 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AYtDvcGs…VuAcA7m7 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.

9.724 × 10⁹⁶(97-digit number)

97247297574048785273…07445004209458867199

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

9.724 × 10⁹⁶(97-digit number)

97247297574048785273…07445004209458867199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.944 × 10⁹⁷(98-digit number)

19449459514809757054…14890008418917734399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.889 × 10⁹⁷(98-digit number)

38898919029619514109…29780016837835468799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.779 × 10⁹⁷(98-digit number)

77797838059239028219…59560033675670937599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.555 × 10⁹⁸(99-digit number)

15559567611847805643…19120067351341875199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.111 × 10⁹⁸(99-digit number)

31119135223695611287…38240134702683750399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.223 × 10⁹⁸(99-digit number)

62238270447391222575…76480269405367500799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.244 × 10⁹⁹(100-digit number)

12447654089478244515…52960538810735001599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.489 × 10⁹⁹(100-digit number)

24895308178956489030…05921077621470003199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.979 × 10⁹⁹(100-digit number)

49790616357912978060…11842155242940006399

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