Block #1,348,764

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.

1.293 × 10⁹⁷(98-digit number)

12934140068702665134…33160416751511039999

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

1.293 × 10⁹⁷(98-digit number)

12934140068702665134…33160416751511039999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.586 × 10⁹⁷(98-digit number)

25868280137405330269…66320833503022079999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.173 × 10⁹⁷(98-digit number)

51736560274810660538…32641667006044159999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.034 × 10⁹⁸(99-digit number)

10347312054962132107…65283334012088319999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.069 × 10⁹⁸(99-digit number)

20694624109924264215…30566668024176639999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.138 × 10⁹⁸(99-digit number)

41389248219848528430…61133336048353279999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.277 × 10⁹⁸(99-digit number)

82778496439697056861…22266672096706559999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.655 × 10⁹⁹(100-digit number)

16555699287939411372…44533344193413119999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.311 × 10⁹⁹(100-digit number)

33111398575878822744…89066688386826239999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.622 × 10⁹⁹(100-digit number)

66222797151757645489…78133376773652479999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

1.324 × 10¹⁰⁰(101-digit number)

13244559430351529097…56266753547304959999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

2.648 × 10¹⁰⁰(101-digit number)

26489118860703058195…12533507094609919999

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

Block #1,348,764

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