Block #854,243

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.

8.686 × 10⁹⁴(95-digit number)

86868859085259049614…46956878953707366679

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

8.686 × 10⁹⁴(95-digit number)

86868859085259049614…46956878953707366679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.737 × 10⁹⁵(96-digit number)

17373771817051809922…93913757907414733359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.474 × 10⁹⁵(96-digit number)

34747543634103619845…87827515814829466719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.949 × 10⁹⁵(96-digit number)

69495087268207239691…75655031629658933439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.389 × 10⁹⁶(97-digit number)

13899017453641447938…51310063259317866879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.779 × 10⁹⁶(97-digit number)

27798034907282895876…02620126518635733759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.559 × 10⁹⁶(97-digit number)

55596069814565791753…05240253037271467519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.111 × 10⁹⁷(98-digit number)

11119213962913158350…10480506074542935039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.223 × 10⁹⁷(98-digit number)

22238427925826316701…20961012149085870079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.447 × 10⁹⁷(98-digit number)

44476855851652633402…41922024298171740159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

8.895 × 10⁹⁷(98-digit number)

88953711703305266805…83844048596343480319

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #854,243

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