Block #459,899

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/25/2014, 2:55:37 PM · Difficulty 10.4215 · 6,355,081 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e46b26bd6e96fc7f17f94a64dd5be788bbbd63b904e59a53ea3f60490e53df2

View on Chainz ↗

Height

#459,899

Difficulty

10.421534

Transactions

Size

2.04 KB

Version

Bits

0a6be9a2

Nonce

1,900

Timestamp

3/25/2014, 2:55:37 PM

Confirmations

6,355,081

Mined by

⛏️ {aS1MAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

aab1e04be0e1269e502f62167e5f3ba2c0d09f8a15f324e721f2b25b3f0fa119

Transactions (2)

Coinbase24f49ae65a8ba8…1de5df860ef524

1 in → 25 out9.1900 XPM913 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AQv2iMwd…EFna22ee AJtNW28X…Syb4Ph5j

538ecb850ec601…779fed2f95bed3

5 in → 15 out45.9900 XPM1.06 KB

ARzHesco…Jx5DU3DY AFqwEJFf…zqg3ZgE6 AXw6mEKq…fKqEjtEj AWq6vDNx…FMFpMcN1 AGaij5dN…mmh48Z5W

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.

1.578 × 10⁹⁷(98-digit number)

15788433309726576456…54286585966736051719

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

1.578 × 10⁹⁷(98-digit number)

15788433309726576456…54286585966736051719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.578 × 10⁹⁷(98-digit number)

15788433309726576456…54286585966736051721

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

3.157 × 10⁹⁷(98-digit number)

31576866619453152912…08573171933472103439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.157 × 10⁹⁷(98-digit number)

31576866619453152912…08573171933472103441

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

6.315 × 10⁹⁷(98-digit number)

63153733238906305824…17146343866944206879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.315 × 10⁹⁷(98-digit number)

63153733238906305824…17146343866944206881

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

1.263 × 10⁹⁸(99-digit number)

12630746647781261164…34292687733888413759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.263 × 10⁹⁸(99-digit number)

12630746647781261164…34292687733888413761

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

2.526 × 10⁹⁸(99-digit number)

25261493295562522329…68585375467776827519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.526 × 10⁹⁸(99-digit number)

25261493295562522329…68585375467776827521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.052 × 10⁹⁸(99-digit number)

50522986591125044659…37170750935553655039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #459,899

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