Block #460,017

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/25/2014, 4:55:33 PM · Difficulty 10.4215 · 6,346,856 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cfbb724c6cca82580eea421f6f4c97836c5b07657327f4612381a5ccfef36417

View on Chainz ↗

Height

#460,017

Difficulty

10.421515

Transactions

Size

1003 B

Version

Bits

0a6be864

Nonce

298,570

Timestamp

3/25/2014, 4:55:33 PM

Confirmations

6,346,856

Mined by

⛏️ aS1AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

4a53d90af081a3744d4757d3c6a5ff3d161806a814fcfc8bad3731536fe4f8c1

Transactions (1)

Coinbase4a53d90af081a3…3731536fe4f8c1

1 in → 25 out9.1900 XPM913 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j ALqxX1WA…hsKjbnXn AKzkYQaQ…zR4FspJZ

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.

1.301 × 10⁹⁴(95-digit number)

13016580129500302189…84337520900650314239

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

1.301 × 10⁹⁴(95-digit number)

13016580129500302189…84337520900650314239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.301 × 10⁹⁴(95-digit number)

13016580129500302189…84337520900650314241

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

2.603 × 10⁹⁴(95-digit number)

26033160259000604378…68675041801300628479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.603 × 10⁹⁴(95-digit number)

26033160259000604378…68675041801300628481

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

5.206 × 10⁹⁴(95-digit number)

52066320518001208756…37350083602601256959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.206 × 10⁹⁴(95-digit number)

52066320518001208756…37350083602601256961

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

1.041 × 10⁹⁵(96-digit number)

10413264103600241751…74700167205202513919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.041 × 10⁹⁵(96-digit number)

10413264103600241751…74700167205202513921

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

2.082 × 10⁹⁵(96-digit number)

20826528207200483502…49400334410405027839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.082 × 10⁹⁵(96-digit number)

20826528207200483502…49400334410405027841

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 #460,017

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