Block #792,865

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.

4.014 × 10⁹⁷(98-digit number)

40145223736179428644…49017095064260839681

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

4.014 × 10⁹⁷(98-digit number)

40145223736179428644…49017095064260839681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.029 × 10⁹⁷(98-digit number)

80290447472358857289…98034190128521679361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.605 × 10⁹⁸(99-digit number)

16058089494471771457…96068380257043358721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.211 × 10⁹⁸(99-digit number)

32116178988943542915…92136760514086717441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.423 × 10⁹⁸(99-digit number)

64232357977887085831…84273521028173434881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.284 × 10⁹⁹(100-digit number)

12846471595577417166…68547042056346869761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.569 × 10⁹⁹(100-digit number)

25692943191154834332…37094084112693739521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.138 × 10⁹⁹(100-digit number)

51385886382309668665…74188168225387479041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.027 × 10¹⁰⁰(101-digit number)

10277177276461933733…48376336450774958081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.055 × 10¹⁰⁰(101-digit number)

20554354552923867466…96752672901549916161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

4.110 × 10¹⁰⁰(101-digit number)

41108709105847734932…93505345803099832321

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 #792,865

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