Block #239,047

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/1/2013, 9:07:52 PM · Difficulty 9.9538 · 6,578,933 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9421a43ea21f0f73d8452bf1dc582a613935282733f4281d07b5d8e1d1239370

View on Chainz ↗

Height

#239,047

Difficulty

9.953759

Transactions

Size

198 B

Version

Bits

09f42986

Nonce

10,047

Timestamp

11/1/2013, 9:07:52 PM

Confirmations

6,578,933

Mined by

⛏️ P2SHAP9Q5TCMUwhVhxfrLF1mfn2PmSn3e5pxk8

Merkle Root

80928f923a43fe225136224d22dc9d9af31f30adc1ae1db272f66435a8ba8c13

Transactions (1)

Coinbase80928f923a43fe…f66435a8ba8c13

1 in → 1 out10.0800 XPM109 B

AP9Q5TCM…n3e5pxk8

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.

1.944 × 10⁹¹(92-digit number)

19447239441243974442…61525030702506987099

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

1.944 × 10⁹¹(92-digit number)

19447239441243974442…61525030702506987099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.944 × 10⁹¹(92-digit number)

19447239441243974442…61525030702506987101

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

3.889 × 10⁹¹(92-digit number)

38894478882487948884…23050061405013974199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.889 × 10⁹¹(92-digit number)

38894478882487948884…23050061405013974201

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

7.778 × 10⁹¹(92-digit number)

77788957764975897769…46100122810027948399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.778 × 10⁹¹(92-digit number)

77788957764975897769…46100122810027948401

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

1.555 × 10⁹²(93-digit number)

15557791552995179553…92200245620055896799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.555 × 10⁹²(93-digit number)

15557791552995179553…92200245620055896801

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

3.111 × 10⁹²(93-digit number)

31115583105990359107…84400491240111793599

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 #239,047

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