Block #429,660

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/4/2014, 10:53:14 PM · Difficulty 10.3458 · 6,369,272 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8959d6c2db3083ad4ade873505bdda8834a09c8fb911f3d83767400b0c40f22e

View on Chainz ↗

Height

#429,660

Difficulty

10.345786

Transactions

Size

1.05 KB

Version

Bits

0a58856b

Nonce

15,840

Timestamp

3/4/2014, 10:53:14 PM

Confirmations

6,369,272

Mined by

⛏️ \aSYGAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

6eea0e0caf850386be5c3df5741af1d9e01605c1b19a6ca9804bb6d2d956358d

Transactions (1)

Coinbase6eea0e0caf8503…4bb6d2d956358d

1 in → 27 out9.3300 XPM981 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

3.634 × 10⁹⁹(100-digit number)

36343095787617413549…78223591536193727679

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

3.634 × 10⁹⁹(100-digit number)

36343095787617413549…78223591536193727679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.268 × 10⁹⁹(100-digit number)

72686191575234827099…56447183072387455359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.453 × 10¹⁰⁰(101-digit number)

14537238315046965419…12894366144774910719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.907 × 10¹⁰⁰(101-digit number)

29074476630093930839…25788732289549821439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.814 × 10¹⁰⁰(101-digit number)

58148953260187861679…51577464579099642879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.162 × 10¹⁰¹(102-digit number)

11629790652037572335…03154929158199285759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.325 × 10¹⁰¹(102-digit number)

23259581304075144671…06309858316398571519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.651 × 10¹⁰¹(102-digit number)

46519162608150289343…12619716632797143039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.303 × 10¹⁰¹(102-digit number)

93038325216300578687…25239433265594286079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.860 × 10¹⁰²(103-digit number)

18607665043260115737…50478866531188572159

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