Block #922,313

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.

3.942 × 10⁹⁷(98-digit number)

39425436069231751093…17115548716419379199

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

3.942 × 10⁹⁷(98-digit number)

39425436069231751093…17115548716419379199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.885 × 10⁹⁷(98-digit number)

78850872138463502186…34231097432838758399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.577 × 10⁹⁸(99-digit number)

15770174427692700437…68462194865677516799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.154 × 10⁹⁸(99-digit number)

31540348855385400874…36924389731355033599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.308 × 10⁹⁸(99-digit number)

63080697710770801749…73848779462710067199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.261 × 10⁹⁹(100-digit number)

12616139542154160349…47697558925420134399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.523 × 10⁹⁹(100-digit number)

25232279084308320699…95395117850840268799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.046 × 10⁹⁹(100-digit number)

50464558168616641399…90790235701680537599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.009 × 10¹⁰⁰(101-digit number)

10092911633723328279…81580471403361075199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.018 × 10¹⁰⁰(101-digit number)

20185823267446656559…63160942806722150399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

4.037 × 10¹⁰⁰(101-digit number)

40371646534893313119…26321885613444300799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

8.074 × 10¹⁰⁰(101-digit number)

80743293069786626239…52643771226888601599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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