Block #290,967

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 10:55:50 PM · Difficulty 9.9896 · 6,515,688 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76b8458f7b054e156947461453e3338d2534e98409f7229d982a71e868bb7898

View on Chainz ↗

Height

#290,967

Difficulty

9.989576

Transactions

Size

1.18 KB

Version

Bits

09fd54e0

Nonce

6,433

Timestamp

12/2/2013, 10:55:50 PM

Confirmations

6,515,688

Mined by

⛏️ paRAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

7a7e6138b6ae6d3e30a4fada072a8a4991306c367d29cbd74e26eed4520d2e10

Transactions (1)

Coinbase7a7e6138b6ae6d…26eed4520d2e10

1 in → 31 out9.9900 XPM1.09 KB

AZninDSu…FvgDMwC4 Ad9pSzHt…cpJ3y2zz AVss9H5F…zXhyMijY AWGQhzDN…RDYvugUy AdpQ3tBd…BCXM7k1Y

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.

1.127 × 10⁹⁵(96-digit number)

11277367618155270918…47640544261226947839

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

1.127 × 10⁹⁵(96-digit number)

11277367618155270918…47640544261226947839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.127 × 10⁹⁵(96-digit number)

11277367618155270918…47640544261226947841

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

2.255 × 10⁹⁵(96-digit number)

22554735236310541837…95281088522453895679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.255 × 10⁹⁵(96-digit number)

22554735236310541837…95281088522453895681

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

4.510 × 10⁹⁵(96-digit number)

45109470472621083675…90562177044907791359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.510 × 10⁹⁵(96-digit number)

45109470472621083675…90562177044907791361

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

9.021 × 10⁹⁵(96-digit number)

90218940945242167350…81124354089815582719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.021 × 10⁹⁵(96-digit number)

90218940945242167350…81124354089815582721

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

1.804 × 10⁹⁶(97-digit number)

18043788189048433470…62248708179631165439

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 #290,967

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