Block #389,078

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2014, 6:38:04 AM · Difficulty 10.4151 · 6,406,538 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

87597b8e735115f3aa08b0aaa70a25d56fc4953697ca07c071172ba5ef5396cb

View on Chainz ↗

Height

#389,078

Difficulty

10.415137

Transactions

Size

797 B

Version

Bits

0a6a466a

Nonce

89,988

Timestamp

2/4/2014, 6:38:04 AM

Confirmations

6,406,538

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a11e0c5119a69e2aeb5be1ca90ff8ddfeaaf0b1eff1e5ca5532ed0ce8032becc

Transactions (1)

Coinbasea11e0c5119a69e…2ed0ce8032becc

1 in → 19 out9.2000 XPM708 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AVv7hVkp…UTbVGddP

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.

1.840 × 10⁹³(94-digit number)

18404441042006886533…97194783482943952399

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

1.840 × 10⁹³(94-digit number)

18404441042006886533…97194783482943952399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.680 × 10⁹³(94-digit number)

36808882084013773067…94389566965887904799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.361 × 10⁹³(94-digit number)

73617764168027546135…88779133931775809599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.472 × 10⁹⁴(95-digit number)

14723552833605509227…77558267863551619199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.944 × 10⁹⁴(95-digit number)

29447105667211018454…55116535727103238399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.889 × 10⁹⁴(95-digit number)

58894211334422036908…10233071454206476799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.177 × 10⁹⁵(96-digit number)

11778842266884407381…20466142908412953599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.355 × 10⁹⁵(96-digit number)

23557684533768814763…40932285816825907199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.711 × 10⁹⁵(96-digit number)

47115369067537629526…81864571633651814399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.423 × 10⁹⁵(96-digit number)

94230738135075259053…63729143267303628799

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