Block #557,901

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/23/2014, 6:16:39 AM · Difficulty 10.9631 · 6,268,668 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0e59437167d05a5f4ed8911b535c5f1a0b7e698f8364e66c23bc4f56d306e4f5

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Height

#557,901

Difficulty

10.963087

Transactions

Size

243 B

Version

Bits

0af68ce5

Nonce

180,334,634

Timestamp

5/23/2014, 6:16:39 AM

Confirmations

6,268,668

Mined by

⛏️ P2SHARPJp62WCtEnziwgi1JL6trLk6RriPibvN

Merkle Root

36c966d9634c63593d3348674513b25b172a1fcae7e4620ab7296763241de65e

Transactions (1)

Coinbase36c966d9634c63…296763241de65e

1 in → 2 out8.3100 XPM152 B

ARPJp62W…RriPibvN ALPu3s2c…EJXLjVFh

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.

7.975 × 10⁹⁷(98-digit number)

79750105934791725941…22994121769046870879

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

7.975 × 10⁹⁷(98-digit number)

79750105934791725941…22994121769046870879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.595 × 10⁹⁸(99-digit number)

15950021186958345188…45988243538093741759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.190 × 10⁹⁸(99-digit number)

31900042373916690376…91976487076187483519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.380 × 10⁹⁸(99-digit number)

63800084747833380753…83952974152374967039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.276 × 10⁹⁹(100-digit number)

12760016949566676150…67905948304749934079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.552 × 10⁹⁹(100-digit number)

25520033899133352301…35811896609499868159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.104 × 10⁹⁹(100-digit number)

51040067798266704602…71623793218999736319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.020 × 10¹⁰⁰(101-digit number)

10208013559653340920…43247586437999472639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.041 × 10¹⁰⁰(101-digit number)

20416027119306681841…86495172875998945279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.083 × 10¹⁰⁰(101-digit number)

40832054238613363682…72990345751997890559

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

Block #557,901

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