Block #254,432

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/10/2013, 5:26:39 PM · Difficulty 9.9731 · 6,538,232 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ea02335276c3e7973e696a91c7d03e764e306f8d40b0fd7665b1b9d037a75f4e

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Height

#254,432

Difficulty

9.973120

Transactions

Size

674 B

Version

Bits

09f91e5f

Nonce

193,204

Timestamp

11/10/2013, 5:26:39 PM

Confirmations

6,538,232

Merkle Root

d8db48b2e101f6c6721cb1d6bf868d0c5c7f35075222bbdaca29f981882095fe

Transactions (2)

Coinbase15f7c514e93112…8972bcd4420330

1 in → 1 out10.0500 XPM110 B

AMa2WoKe…RgX4EdWb

3238b965f5848c…1e64865cae72b1

2 in → 7 out20.1500 XPM476 B

ARitzeAs…zBHrD3ss AHb9D17o…rg9iXrZC AeKNrjNj…1NEq95Ta ARtPXKuc…KzX35CG6 AbNgL8yS…Wu6nPFk5

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.

2.905 × 10⁹⁰(91-digit number)

29053500578909419883…18596343171647905159

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

2.905 × 10⁹⁰(91-digit number)

29053500578909419883…18596343171647905159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.810 × 10⁹⁰(91-digit number)

58107001157818839767…37192686343295810319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.162 × 10⁹¹(92-digit number)

11621400231563767953…74385372686591620639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.324 × 10⁹¹(92-digit number)

23242800463127535907…48770745373183241279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.648 × 10⁹¹(92-digit number)

46485600926255071814…97541490746366482559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.297 × 10⁹¹(92-digit number)

92971201852510143628…95082981492732965119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.859 × 10⁹²(93-digit number)

18594240370502028725…90165962985465930239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.718 × 10⁹²(93-digit number)

37188480741004057451…80331925970931860479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.437 × 10⁹²(93-digit number)

74376961482008114902…60663851941863720959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.487 × 10⁹³(94-digit number)

14875392296401622980…21327703883727441919

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