Block #276,508

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 5:15:13 AM · Difficulty 9.9634 · 6,529,852 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

49727099c4b1c988ef7b270b92d5023e80f7e6b22b2d723506bd4bf6b37beefc

View on Chainz ↗

Height

#276,508

Difficulty

9.963355

Transactions

Size

1.15 KB

Version

Bits

09f69e70

Nonce

130,188

Timestamp

11/27/2013, 5:15:13 AM

Confirmations

6,529,852

Mined by

⛏️ 8aRASPzomextjr27SzafPpfmLEEfdJkjSwA1z

Merkle Root

174a1141ae5fed7ad71fb7d052749538a0bf2a2cbede2bfd4e4800c5bec10147

Transactions (1)

Coinbase174a1141ae5fed…4800c5bec10147

1 in → 30 out10.0400 XPM1.06 KB

ASPzomex…JkjSwA1z AWNm5iN2…RrkMw1vi AaZptiTm…mxymWwAJ Abv8pzf1…t4zPXDTV AXzcEfhQ…Dz9wL2mD

Prime Chain Origin

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.

6.996 × 10⁹⁴(95-digit number)

69967566031287747592…12461993547942453119

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

6.996 × 10⁹⁴(95-digit number)

69967566031287747592…12461993547942453119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.996 × 10⁹⁴(95-digit number)

69967566031287747592…12461993547942453121

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

1.399 × 10⁹⁵(96-digit number)

13993513206257549518…24923987095884906239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.399 × 10⁹⁵(96-digit number)

13993513206257549518…24923987095884906241

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

2.798 × 10⁹⁵(96-digit number)

27987026412515099037…49847974191769812479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.798 × 10⁹⁵(96-digit number)

27987026412515099037…49847974191769812481

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

5.597 × 10⁹⁵(96-digit number)

55974052825030198074…99695948383539624959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.597 × 10⁹⁵(96-digit number)

55974052825030198074…99695948383539624961

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

1.119 × 10⁹⁶(97-digit number)

11194810565006039614…99391896767079249919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #276,508

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