Block #289,291

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 3:29:20 AM · Difficulty 9.9884 · 6,508,576 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

77106cbfdf1ed6d82d5dc01f0c59f8f198377ee4d1788fb759cba781e88ea9a8

View on Chainz ↗

Height

#289,291

Difficulty

9.988411

Transactions

Size

1.15 KB

Version

Bits

09fd0879

Nonce

27,819

Timestamp

12/2/2013, 3:29:20 AM

Confirmations

6,508,576

Mined by

⛏️ jaRAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

50d450234dba19d1d2d380e5ee8727b9c857079e8273dc4354a76a4ee81ce37c

Transactions (1)

Coinbase50d450234dba19…a76a4ee81ce37c

1 in → 30 out9.9900 XPM1.06 KB

AYcLTeXR…bscgPops AdyKWr2A…7PSnFqeJ AdCxxeng…JqmRFhac Acs9SHrk…QJSB8SFG Ac6mGvmQ…XqWmPHjR

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.

1.094 × 10⁹⁸(99-digit number)

10940775218456089311…97138157226245476799

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

1.094 × 10⁹⁸(99-digit number)

10940775218456089311…97138157226245476799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.094 × 10⁹⁸(99-digit number)

10940775218456089311…97138157226245476801

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

2.188 × 10⁹⁸(99-digit number)

21881550436912178622…94276314452490953599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.188 × 10⁹⁸(99-digit number)

21881550436912178622…94276314452490953601

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

4.376 × 10⁹⁸(99-digit number)

43763100873824357244…88552628904981907199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.376 × 10⁹⁸(99-digit number)

43763100873824357244…88552628904981907201

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

8.752 × 10⁹⁸(99-digit number)

87526201747648714489…77105257809963814399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.752 × 10⁹⁸(99-digit number)

87526201747648714489…77105257809963814401

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

1.750 × 10⁹⁹(100-digit number)

17505240349529742897…54210515619927628799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.750 × 10⁹⁹(100-digit number)

17505240349529742897…54210515619927628801

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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