Block #289,180

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 2:10:23 AM · Difficulty 9.9883 · 6,527,643 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

863762ecc356d3f566746df7e9fafd45293c8eaf4b68c26ffed02a0db0ab4632

View on Chainz ↗

Height

#289,180

Difficulty

9.988328

Transactions

Size

972 B

Version

Bits

09fd0309

Nonce

8,124

Timestamp

12/2/2013, 2:10:23 AM

Confirmations

6,527,643

Mined by

⛏️ iaRJAFuakYLnxFs7PgaWe4P452CULexnY8QBEG

Merkle Root

0bc4c0668be8fef4bde7d92a9dfd810fc7bc1797e9db9668b6612a6b3e997dfb

Transactions (1)

Coinbase0bc4c0668be8fe…612a6b3e997dfb

1 in → 24 out10.0100 XPM879 B

AFuakYLn…xnY8QBEG APzJyfoN…Lg7ShKEF AenXgLL6…ChwZjYpX AYcLTeXR…bscgPops AWA5FEzr…x9RdPKTy

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.

7.795 × 10¹⁰⁰(101-digit number)

77956786113637055826…88494865254142649489

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

7.795 × 10¹⁰⁰(101-digit number)

77956786113637055826…88494865254142649489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.795 × 10¹⁰⁰(101-digit number)

77956786113637055826…88494865254142649491

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

1.559 × 10¹⁰¹(102-digit number)

15591357222727411165…76989730508285298979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.559 × 10¹⁰¹(102-digit number)

15591357222727411165…76989730508285298981

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

3.118 × 10¹⁰¹(102-digit number)

31182714445454822330…53979461016570597959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.118 × 10¹⁰¹(102-digit number)

31182714445454822330…53979461016570597961

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

6.236 × 10¹⁰¹(102-digit number)

62365428890909644661…07958922033141195919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.236 × 10¹⁰¹(102-digit number)

62365428890909644661…07958922033141195921

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

1.247 × 10¹⁰²(103-digit number)

12473085778181928932…15917844066282391839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.247 × 10¹⁰²(103-digit number)

12473085778181928932…15917844066282391841

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

Block #289,180

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