Block #529,360

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.

1.299 × 10⁹⁸(99-digit number)

12990668760271924347…15433941686865207011

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

1.299 × 10⁹⁸(99-digit number)

12990668760271924347…15433941686865207011

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.598 × 10⁹⁸(99-digit number)

25981337520543848694…30867883373730414021

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.196 × 10⁹⁸(99-digit number)

51962675041087697389…61735766747460828041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.039 × 10⁹⁹(100-digit number)

10392535008217539477…23471533494921656081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.078 × 10⁹⁹(100-digit number)

20785070016435078955…46943066989843312161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.157 × 10⁹⁹(100-digit number)

41570140032870157911…93886133979686624321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.314 × 10⁹⁹(100-digit number)

83140280065740315823…87772267959373248641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.662 × 10¹⁰⁰(101-digit number)

16628056013148063164…75544535918746497281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.325 × 10¹⁰⁰(101-digit number)

33256112026296126329…51089071837492994561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.651 × 10¹⁰⁰(101-digit number)

66512224052592252658…02178143674985989121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.330 × 10¹⁰¹(102-digit number)

13302444810518450531…04356287349971978241

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #529,360

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