Block #459,851

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/25/2014, 2:12:25 PM · Difficulty 10.4210 · 6,346,361 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

31667786e737e169e76e226ff33617052a6963a2656f7344e544e6519f26a06f

View on Chainz ↗

Height

#459,851

Difficulty

10.420955

Transactions

Size

901 B

Version

Bits

0a6bc3b5

Nonce

32,486

Timestamp

3/25/2014, 2:12:25 PM

Confirmations

6,346,361

Mined by

⛏️ KaS1XAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3820163c6c2fef09f7ccd6e185c85aff20b48af1f35592bda6a7727f4ce1ddf4

Transactions (1)

Coinbase3820163c6c2fef…a7727f4ce1ddf4

1 in → 22 out9.1900 XPM811 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AJtNW28X…Syb4Ph5j AScAzqGc…BZ6tV1vJ

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.

6.816 × 10⁹⁴(95-digit number)

68162348339671459263…89942386323711745599

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

6.816 × 10⁹⁴(95-digit number)

68162348339671459263…89942386323711745599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.363 × 10⁹⁵(96-digit number)

13632469667934291852…79884772647423491199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.726 × 10⁹⁵(96-digit number)

27264939335868583705…59769545294846982399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.452 × 10⁹⁵(96-digit number)

54529878671737167410…19539090589693964799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.090 × 10⁹⁶(97-digit number)

10905975734347433482…39078181179387929599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.181 × 10⁹⁶(97-digit number)

21811951468694866964…78156362358775859199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.362 × 10⁹⁶(97-digit number)

43623902937389733928…56312724717551718399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.724 × 10⁹⁶(97-digit number)

87247805874779467856…12625449435103436799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.744 × 10⁹⁷(98-digit number)

17449561174955893571…25250898870206873599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.489 × 10⁹⁷(98-digit number)

34899122349911787142…50501797740413747199

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