Block #385,687

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2014, 11:18:00 PM · Difficulty 10.4054 · 6,406,897 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ffefc7d4f2592af00b089c850bc21e9e5fd44ae3f149c6c82ae0e2c243081016

View on Chainz ↗

Height

#385,687

Difficulty

10.405377

Transactions

Size

1.29 KB

Version

Bits

0a67c6cf

Nonce

157,393

Timestamp

2/1/2014, 11:18:00 PM

Confirmations

6,406,897

Merkle Root

93a96094226ac2ae10005ef9038d8baa19e9b49a4f904e2ec6af0b2f6ddd8f03

Transactions (2)

Coinbase9199270f248c34…51655ca03b43c9

1 in → 1 out9.2400 XPM110 B

AeKNrjNj…1NEq95Ta

0f20cd40abbede…73cf0b0d44b0ca

7 in → 2 out33.9720 XPM1.09 KB

ASLD47Zx…pDXXpnD4 AbMPqavc…w5Vpu6pA

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.

3.455 × 10¹⁰¹(102-digit number)

34559203261391863930…54206562221800543759

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

3.455 × 10¹⁰¹(102-digit number)

34559203261391863930…54206562221800543759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.455 × 10¹⁰¹(102-digit number)

34559203261391863930…54206562221800543761

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

6.911 × 10¹⁰¹(102-digit number)

69118406522783727861…08413124443601087519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.911 × 10¹⁰¹(102-digit number)

69118406522783727861…08413124443601087521

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

1.382 × 10¹⁰²(103-digit number)

13823681304556745572…16826248887202175039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.382 × 10¹⁰²(103-digit number)

13823681304556745572…16826248887202175041

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

2.764 × 10¹⁰²(103-digit number)

27647362609113491144…33652497774404350079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.764 × 10¹⁰²(103-digit number)

27647362609113491144…33652497774404350081

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

5.529 × 10¹⁰²(103-digit number)

55294725218226982288…67304995548808700159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.529 × 10¹⁰²(103-digit number)

55294725218226982288…67304995548808700161

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