Block #2,646,080

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.

4.981 × 10⁹⁴(95-digit number)

49813364341587100410…07650943937050787841

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

4.981 × 10⁹⁴(95-digit number)

49813364341587100410…07650943937050787841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.962 × 10⁹⁴(95-digit number)

99626728683174200820…15301887874101575681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.992 × 10⁹⁵(96-digit number)

19925345736634840164…30603775748203151361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.985 × 10⁹⁵(96-digit number)

39850691473269680328…61207551496406302721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.970 × 10⁹⁵(96-digit number)

79701382946539360656…22415102992812605441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.594 × 10⁹⁶(97-digit number)

15940276589307872131…44830205985625210881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.188 × 10⁹⁶(97-digit number)

31880553178615744262…89660411971250421761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.376 × 10⁹⁶(97-digit number)

63761106357231488525…79320823942500843521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.275 × 10⁹⁷(98-digit number)

12752221271446297705…58641647885001687041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.550 × 10⁹⁷(98-digit number)

25504442542892595410…17283295770003374081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

5.100 × 10⁹⁷(98-digit number)

51008885085785190820…34566591540006748161

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 #2,646,080

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