Block #2,995,577

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.

9.968 × 10⁹⁶(97-digit number)

99681193273542857793…33894761046991902719

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 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.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

9.968 × 10⁹⁶(97-digit number)

99681193273542857793…33894761046991902719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.968 × 10⁹⁶(97-digit number)

99681193273542857793…33894761046991902721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.993 × 10⁹⁷(98-digit number)

19936238654708571558…67789522093983805439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.993 × 10⁹⁷(98-digit number)

19936238654708571558…67789522093983805441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.987 × 10⁹⁷(98-digit number)

39872477309417143117…35579044187967610879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.987 × 10⁹⁷(98-digit number)

39872477309417143117…35579044187967610881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

7.974 × 10⁹⁷(98-digit number)

79744954618834286235…71158088375935221759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.974 × 10⁹⁷(98-digit number)

79744954618834286235…71158088375935221761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.594 × 10⁹⁸(99-digit number)

15948990923766857247…42316176751870443519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.594 × 10⁹⁸(99-digit number)

15948990923766857247…42316176751870443521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.189 × 10⁹⁸(99-digit number)

31897981847533714494…84632353503740887039

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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,995,577

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