Block #382,364

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/30/2014, 3:49:55 PM · Difficulty 10.4044 · 6,416,611 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ff79b0f2b4e8cd316486e35b631dd2f26c721cf8b911a50cff37cddd7b6c8ec8

View on Chainz ↗

Height

#382,364

Difficulty

10.404443

Transactions

Size

398 B

Version

Bits

0a67898c

Nonce

8,383

Timestamp

1/30/2014, 3:49:55 PM

Confirmations

6,416,611

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

356dedc450801b8cc82938799cf4dc5760cb614b98c2f263e2164c8569e334b6

Transactions (2)

Coinbase142c2a0f6b7c02…1c5dcaf094e1e7

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

e8dec02f303b3d…db44c8e69a31a1

1 in → 1 out3.1058 XPM191 B

AGyExqaw…hEupTgHL

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.

3.738 × 10⁹⁷(98-digit number)

37383737774940056703…97158868367500994559

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

3.738 × 10⁹⁷(98-digit number)

37383737774940056703…97158868367500994559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.476 × 10⁹⁷(98-digit number)

74767475549880113406…94317736735001989119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.495 × 10⁹⁸(99-digit number)

14953495109976022681…88635473470003978239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.990 × 10⁹⁸(99-digit number)

29906990219952045362…77270946940007956479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.981 × 10⁹⁸(99-digit number)

59813980439904090725…54541893880015912959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.196 × 10⁹⁹(100-digit number)

11962796087980818145…09083787760031825919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.392 × 10⁹⁹(100-digit number)

23925592175961636290…18167575520063651839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.785 × 10⁹⁹(100-digit number)

47851184351923272580…36335151040127303679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.570 × 10⁹⁹(100-digit number)

95702368703846545160…72670302080254607359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.914 × 10¹⁰⁰(101-digit number)

19140473740769309032…45340604160509214719

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