Block #470,171

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 5:29:43 PM · Difficulty 10.4319 · 6,339,711 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

77f580fa7dff176ebab6e54d76b4d12d3efa34d082c20f57a705e61ef0536c0a

View on Chainz ↗

Height

#470,171

Difficulty

10.431898

Transactions

Size

1.28 KB

Version

Bits

0a6e90d8

Nonce

58,138

Timestamp

4/1/2014, 5:29:43 PM

Confirmations

6,339,711

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

3a62d3fd217393d7cb52945f0468adbbc5b27dff71a705ad6f3620127de68afa

Transactions (2)

Coinbase24e035db8e01e3…652755397b27e3

1 in → 3 out9.1900 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

8a7c011027bda1…f21404a9378fc2

5 in → 13 out39.5382 XPM1.03 KB

Aam1z35x…d4HdYDK8 ALACS8NF…7JeM6YTm AeKNrjNj…1NEq95Ta Acjw5rzo…872kPK2w AP5i7QoC…HmBrELxR

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.

9.279 × 10⁹⁴(95-digit number)

92790218618380256465…61250885423549397759

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

9.279 × 10⁹⁴(95-digit number)

92790218618380256465…61250885423549397759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.279 × 10⁹⁴(95-digit number)

92790218618380256465…61250885423549397761

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

1.855 × 10⁹⁵(96-digit number)

18558043723676051293…22501770847098795519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.855 × 10⁹⁵(96-digit number)

18558043723676051293…22501770847098795521

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

3.711 × 10⁹⁵(96-digit number)

37116087447352102586…45003541694197591039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.711 × 10⁹⁵(96-digit number)

37116087447352102586…45003541694197591041

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

7.423 × 10⁹⁵(96-digit number)

74232174894704205172…90007083388395182079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.423 × 10⁹⁵(96-digit number)

74232174894704205172…90007083388395182081

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

1.484 × 10⁹⁶(97-digit number)

14846434978940841034…80014166776790364159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.484 × 10⁹⁶(97-digit number)

14846434978940841034…80014166776790364161

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 #470,171

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