Block #1,029,067

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/23/2015, 6:45:18 AM · Difficulty 10.7607 · 5,804,440 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

74babd998cf00fe699bc9171c4f74572f259b0e00aaa8b222d2999103630c3b9

View on Chainz ↗

Height

#1,029,067

Difficulty

10.760669

Transactions

Size

243 B

Version

Bits

0ac2bb2e

Nonce

327,233,357

Timestamp

4/23/2015, 6:45:18 AM

Confirmations

5,804,440

Mined by

⛏️ P2SHAUV3ZXsawxZuaXubcanNHw2sUMP3xQCbyH

Merkle Root

d5d3ba23ae5c28d6709b39622ee9918e974876a4b554a60c23d2c886cf1269f3

Transactions (1)

Coinbased5d3ba23ae5c28…d2c886cf1269f3

1 in → 2 out8.6200 XPM152 B

AUV3ZXsa…P3xQCbyH 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.

1.474 × 10⁹⁸(99-digit number)

14748187766307913221…54097735709152174079

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

1.474 × 10⁹⁸(99-digit number)

14748187766307913221…54097735709152174079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.949 × 10⁹⁸(99-digit number)

29496375532615826443…08195471418304348159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.899 × 10⁹⁸(99-digit number)

58992751065231652887…16390942836608696319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.179 × 10⁹⁹(100-digit number)

11798550213046330577…32781885673217392639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.359 × 10⁹⁹(100-digit number)

23597100426092661154…65563771346434785279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.719 × 10⁹⁹(100-digit number)

47194200852185322309…31127542692869570559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.438 × 10⁹⁹(100-digit number)

94388401704370644619…62255085385739141119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.887 × 10¹⁰⁰(101-digit number)

18877680340874128923…24510170771478282239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.775 × 10¹⁰⁰(101-digit number)

37755360681748257847…49020341542956564479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.551 × 10¹⁰⁰(101-digit number)

75510721363496515695…98040683085913128959

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 #1,029,067

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