Block #392,053

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.

2.218 × 10⁹⁹(100-digit number)

22183461327544173319…24866477267290954241

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

2.218 × 10⁹⁹(100-digit number)

22183461327544173319…24866477267290954241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.436 × 10⁹⁹(100-digit number)

44366922655088346638…49732954534581908481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.873 × 10⁹⁹(100-digit number)

88733845310176693276…99465909069163816961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.774 × 10¹⁰⁰(101-digit number)

17746769062035338655…98931818138327633921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.549 × 10¹⁰⁰(101-digit number)

35493538124070677310…97863636276655267841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.098 × 10¹⁰⁰(101-digit number)

70987076248141354621…95727272553310535681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.419 × 10¹⁰¹(102-digit number)

14197415249628270924…91454545106621071361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.839 × 10¹⁰¹(102-digit number)

28394830499256541848…82909090213242142721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.678 × 10¹⁰¹(102-digit number)

56789660998513083696…65818180426484285441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.135 × 10¹⁰²(103-digit number)

11357932199702616739…31636360852968570881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.271 × 10¹⁰²(103-digit number)

22715864399405233478…63272721705937141761

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