Block #389,294

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 9:54:17 AM · Difficulty 10.4191 · 6,412,932 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dd55887ff9d2c7dc8155cbd1d788393472aa1e939b599ba2c6ea3ac37bead99f

View on Chainz ↗

Height

#389,294

Difficulty

10.419054

Transactions

Size

1.46 KB

Version

Bits

0a6b4721

Nonce

397,942

Timestamp

2/4/2014, 9:54:17 AM

Confirmations

6,412,932

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e3c18eb9493338237d69b9ca611974846eb0c32a4abd6cb6e9015241e610122f

Transactions (2)

Coinbased643affce3f76d…1e050f6c4445bc

1 in → 24 out9.2000 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ANeHTs9o…oazVAG8Z AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1

b4738543d4aadd…9168e60f931bfe

3 in → 2 out213.6063 XPM523 B

AZb9b8yj…sYB6aNaQ ALyTjd7V…Y1hUJpRK

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.

1.625 × 10¹⁰⁰(101-digit number)

16252555781223255784…64502325875186022199

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

1.625 × 10¹⁰⁰(101-digit number)

16252555781223255784…64502325875186022199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.625 × 10¹⁰⁰(101-digit number)

16252555781223255784…64502325875186022201

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

3.250 × 10¹⁰⁰(101-digit number)

32505111562446511568…29004651750372044399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.250 × 10¹⁰⁰(101-digit number)

32505111562446511568…29004651750372044401

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

6.501 × 10¹⁰⁰(101-digit number)

65010223124893023136…58009303500744088799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.501 × 10¹⁰⁰(101-digit number)

65010223124893023136…58009303500744088801

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

1.300 × 10¹⁰¹(102-digit number)

13002044624978604627…16018607001488177599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.300 × 10¹⁰¹(102-digit number)

13002044624978604627…16018607001488177601

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

2.600 × 10¹⁰¹(102-digit number)

26004089249957209254…32037214002976355199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.600 × 10¹⁰¹(102-digit number)

26004089249957209254…32037214002976355201

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