Block #264,024

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/18/2013, 8:20:33 AM · Difficulty 9.9651 · 6,552,243 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0de800ffa13b3892035e27f0e285b604201d64cde027881ebd3bd2cc4c3be748

View on Chainz ↗

Height

#264,024

Difficulty

9.965076

Transactions

Size

2.39 KB

Version

Bits

09f70f3a

Nonce

299,864

Timestamp

11/18/2013, 8:20:33 AM

Confirmations

6,552,243

Mined by

⛏️ XaR1AKWzAUKc3CbwP8g7QK3LN9KbmHim8rhc8E

Merkle Root

5b8f62dbdde46e2bb0e8f126c97c1d6b1a878bf85f7904ad4d59fcd199934f32

Transactions (2)

Coinbasef34ff61d881ff7…c379a936540070

1 in → 61 out10.0300 XPM2.09 KB

AKWzAUKc…im8rhc8E AFqKfjez…qX9Ace3g APZy8y6E…QZaGQjfp AMttQDuf…7j6tfS9x AN4KokSc…8oFYPA8o

160c55f9a65c90…351b2b4935a856

1 in → 2 out3.9900 XPM226 B

AdDpCkjt…GLUMxKRX Abiv4G9n…aomYvEup

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.

3.762 × 10⁸⁸(89-digit number)

37627107136833520610…17613034541615512819

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

3.762 × 10⁸⁸(89-digit number)

37627107136833520610…17613034541615512819

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.525 × 10⁸⁸(89-digit number)

75254214273667041220…35226069083231025639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.505 × 10⁸⁹(90-digit number)

15050842854733408244…70452138166462051279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.010 × 10⁸⁹(90-digit number)

30101685709466816488…40904276332924102559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.020 × 10⁸⁹(90-digit number)

60203371418933632976…81808552665848205119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.204 × 10⁹⁰(91-digit number)

12040674283786726595…63617105331696410239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.408 × 10⁹⁰(91-digit number)

24081348567573453190…27234210663392820479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.816 × 10⁹⁰(91-digit number)

48162697135146906381…54468421326785640959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.632 × 10⁹⁰(91-digit number)

96325394270293812762…08936842653571281919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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

Block #264,024

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