Block #389,705

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 4:07:47 PM · Difficulty 10.4216 · 6,434,945 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

08b8d97e1c60d85e611d4340b7d14e79e1522c3b80d021ef5b27c8d45c45f839

View on Chainz ↗

Height

#389,705

Difficulty

10.421569

Transactions

Size

1.61 KB

Version

Bits

0a6bebf1

Nonce

45,216

Timestamp

2/4/2014, 4:07:47 PM

Confirmations

6,434,945

Mined by

⛏️ IaRpAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

13e2540db8e1dbd10799f55b2fbb329d7a7f3f34e8a39701f5ba74e461fb6e21

Transactions (4)

Coinbase14485151d0af19…16fc5275ba276f

1 in → 24 out9.1900 XPM879 B

AQvZBsUo…hppgRZTJ AGPYJBwg…5yWMRKmU AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn ARYJiGcH…7eaSxdkL

c59bfed570b253…a1a0bdd3ba5349

1 in → 2 out7.5832 XPM226 B

Ad11bxn9…6abpGoQ6 ATPnoTDM…ozHEMuvW

b61501b20bbc9d…288ba2170200dc

1 in → 2 out2.9187 XPM226 B

AKuyLMCe…Sy2eavA1 AavEdm6u…7ba9Faoj

5ea40c3338fa76…ad5404cb141df6

1 in → 2 out2.9434 XPM226 B

ALhVKLQa…2eyq2gC3 ASfQj9Pb…Q87HBF2g

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.

1.687 × 10⁹⁷(98-digit number)

16875601386807916027…34835016296175815759

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

1.687 × 10⁹⁷(98-digit number)

16875601386807916027…34835016296175815759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.687 × 10⁹⁷(98-digit number)

16875601386807916027…34835016296175815761

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

3.375 × 10⁹⁷(98-digit number)

33751202773615832054…69670032592351631519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.375 × 10⁹⁷(98-digit number)

33751202773615832054…69670032592351631521

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

6.750 × 10⁹⁷(98-digit number)

67502405547231664109…39340065184703263039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.750 × 10⁹⁷(98-digit number)

67502405547231664109…39340065184703263041

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

1.350 × 10⁹⁸(99-digit number)

13500481109446332821…78680130369406526079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.350 × 10⁹⁸(99-digit number)

13500481109446332821…78680130369406526081

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

2.700 × 10⁹⁸(99-digit number)

27000962218892665643…57360260738813052159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.700 × 10⁹⁸(99-digit number)

27000962218892665643…57360260738813052161

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 #389,705

Cookie Preferences