Block #389,009

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 5:47:00 AM · Difficulty 10.4129 · 6,456,321 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49b93570300ee0cac4b20b9a43ca00a8c9180d5538b7528b6725cf0b00fa78a5

View on Chainz ↗

Height

#389,009

Difficulty

10.412873

Transactions

Size

870 B

Version

Bits

0a69b20e

Nonce

118,994

Timestamp

2/4/2014, 5:47:00 AM

Confirmations

6,456,321

Mined by

⛏️ aR~nAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9f5045d6261402db9c7caaab06101eebeaa82e034a80dc8296298ed8f95f0a47

Transactions (1)

Coinbase9f5045d6261402…298ed8f95f0a47

1 in → 21 out9.2100 XPM777 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AVSSoqRA…aFjFn3Zm

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.

8.136 × 10¹⁰¹(102-digit number)

81369718054058566211…58785797609061565439

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

8.136 × 10¹⁰¹(102-digit number)

81369718054058566211…58785797609061565439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.136 × 10¹⁰¹(102-digit number)

81369718054058566211…58785797609061565441

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

1.627 × 10¹⁰²(103-digit number)

16273943610811713242…17571595218123130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.627 × 10¹⁰²(103-digit number)

16273943610811713242…17571595218123130881

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

3.254 × 10¹⁰²(103-digit number)

32547887221623426484…35143190436246261759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.254 × 10¹⁰²(103-digit number)

32547887221623426484…35143190436246261761

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

6.509 × 10¹⁰²(103-digit number)

65095774443246852969…70286380872492523519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.509 × 10¹⁰²(103-digit number)

65095774443246852969…70286380872492523521

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

1.301 × 10¹⁰³(104-digit number)

13019154888649370593…40572761744985047039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.301 × 10¹⁰³(104-digit number)

13019154888649370593…40572761744985047041

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 #389,009

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