Block #227,946

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/26/2013, 5:07:02 AM · Difficulty 9.9372 · 6,579,234 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3fda81f869a577891b1b2bb030fa8e2fb7f11d639bc66a082e3cb64de7bc842d

View on Chainz ↗

Height

#227,946

Difficulty

9.937209

Transactions

Size

1.08 KB

Version

Bits

09efecea

Nonce

245,231

Timestamp

10/26/2013, 5:07:02 AM

Confirmations

6,579,234

Mined by

⛏️ jzRkMAKwqFUdzFNyMbekqhPUpd29CZJD4jGNKFN

Merkle Root

aa2ad459b85216e1dfc6b6667adf6e44d040b2cb37e144fa682d9af3d3388fa7

Transactions (1)

Coinbaseaa2ad459b85216…2d9af3d3388fa7

1 in → 28 out10.0900 XPM1014 B

AKwqFUdz…D4jGNKFN AWxMqAjD…jNai1Anq AFqKfjez…qX9Ace3g AU3PaCwF…92DCmeEV ARpndEmc…Hg792kEk

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.

2.323 × 10⁹⁴(95-digit number)

23236637947009581035…03688726031511029759

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

2.323 × 10⁹⁴(95-digit number)

23236637947009581035…03688726031511029759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.323 × 10⁹⁴(95-digit number)

23236637947009581035…03688726031511029761

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

4.647 × 10⁹⁴(95-digit number)

46473275894019162070…07377452063022059519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.647 × 10⁹⁴(95-digit number)

46473275894019162070…07377452063022059521

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

9.294 × 10⁹⁴(95-digit number)

92946551788038324140…14754904126044119039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.294 × 10⁹⁴(95-digit number)

92946551788038324140…14754904126044119041

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

1.858 × 10⁹⁵(96-digit number)

18589310357607664828…29509808252088238079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.858 × 10⁹⁵(96-digit number)

18589310357607664828…29509808252088238081

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

3.717 × 10⁹⁵(96-digit number)

37178620715215329656…59019616504176476159

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 #227,946

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