Block #305,432

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.

7.551 × 10¹⁰⁰(101-digit number)

75511166793522192990…96287544392178089921

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

7.551 × 10¹⁰⁰(101-digit number)

75511166793522192990…96287544392178089921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.510 × 10¹⁰¹(102-digit number)

15102233358704438598…92575088784356179841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.020 × 10¹⁰¹(102-digit number)

30204466717408877196…85150177568712359681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.040 × 10¹⁰¹(102-digit number)

60408933434817754392…70300355137424719361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.208 × 10¹⁰²(103-digit number)

12081786686963550878…40600710274849438721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.416 × 10¹⁰²(103-digit number)

24163573373927101756…81201420549698877441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.832 × 10¹⁰²(103-digit number)

48327146747854203513…62402841099397754881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.665 × 10¹⁰²(103-digit number)

96654293495708407027…24805682198795509761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.933 × 10¹⁰³(104-digit number)

19330858699141681405…49611364397591019521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.866 × 10¹⁰³(104-digit number)

38661717398283362811…99222728795182039041

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer

Block #305,432

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