Block #2,679,548

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.

4.155 × 10⁹⁸(99-digit number)

41553448543801613220…80143406339359805439

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

4.155 × 10⁹⁸(99-digit number)

41553448543801613220…80143406339359805439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.310 × 10⁹⁸(99-digit number)

83106897087603226441…60286812678719610879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.662 × 10⁹⁹(100-digit number)

16621379417520645288…20573625357439221759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.324 × 10⁹⁹(100-digit number)

33242758835041290576…41147250714878443519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.648 × 10⁹⁹(100-digit number)

66485517670082581152…82294501429756887039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.329 × 10¹⁰⁰(101-digit number)

13297103534016516230…64589002859513774079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.659 × 10¹⁰⁰(101-digit number)

26594207068033032461…29178005719027548159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.318 × 10¹⁰⁰(101-digit number)

53188414136066064922…58356011438055096319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.063 × 10¹⁰¹(102-digit number)

10637682827213212984…16712022876110192639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.127 × 10¹⁰¹(102-digit number)

21275365654426425968…33424045752220385279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

4.255 × 10¹⁰¹(102-digit number)

42550731308852851937…66848091504440770559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

8.510 × 10¹⁰¹(102-digit number)

85101462617705703875…33696183008881541119

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 #2,679,548

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