Block #858,109

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.

7.755 × 10⁹⁷(98-digit number)

77556524056091121269…71252206923916456961

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

7.755 × 10⁹⁷(98-digit number)

77556524056091121269…71252206923916456961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.551 × 10⁹⁸(99-digit number)

15511304811218224253…42504413847832913921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.102 × 10⁹⁸(99-digit number)

31022609622436448507…85008827695665827841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.204 × 10⁹⁸(99-digit number)

62045219244872897015…70017655391331655681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.240 × 10⁹⁹(100-digit number)

12409043848974579403…40035310782663311361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.481 × 10⁹⁹(100-digit number)

24818087697949158806…80070621565326622721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.963 × 10⁹⁹(100-digit number)

49636175395898317612…60141243130653245441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.927 × 10⁹⁹(100-digit number)

99272350791796635225…20282486261306490881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.985 × 10¹⁰⁰(101-digit number)

19854470158359327045…40564972522612981761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.970 × 10¹⁰⁰(101-digit number)

39708940316718654090…81129945045225963521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

7.941 × 10¹⁰⁰(101-digit number)

79417880633437308180…62259890090451927041

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 #858,109

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