Block #2,655,046

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.

2.934 × 10⁹⁴(95-digit number)

29348888988837771837…46446187669036884479

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

2.934 × 10⁹⁴(95-digit number)

29348888988837771837…46446187669036884479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.869 × 10⁹⁴(95-digit number)

58697777977675543674…92892375338073768959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.173 × 10⁹⁵(96-digit number)

11739555595535108734…85784750676147537919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.347 × 10⁹⁵(96-digit number)

23479111191070217469…71569501352295075839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.695 × 10⁹⁵(96-digit number)

46958222382140434939…43139002704590151679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.391 × 10⁹⁵(96-digit number)

93916444764280869879…86278005409180303359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.878 × 10⁹⁶(97-digit number)

18783288952856173975…72556010818360606719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.756 × 10⁹⁶(97-digit number)

37566577905712347951…45112021636721213439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.513 × 10⁹⁶(97-digit number)

75133155811424695903…90224043273442426879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.502 × 10⁹⁷(98-digit number)

15026631162284939180…80448086546884853759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

3.005 × 10⁹⁷(98-digit number)

30053262324569878361…60896173093769707519

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 #2,655,046

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