Block #460,487

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 1:34:17 AM · Difficulty 10.4164 · 6,376,363 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d87d30537426d1d31d15b49f0a71ef5bbec42b9eaf4512f13c525e1d808c6c09

View on Chainz ↗

Height

#460,487

Difficulty

10.416371

Transactions

Size

662 B

Version

Bits

0a6a9751

Nonce

23,040

Timestamp

3/26/2014, 1:34:17 AM

Confirmations

6,376,363

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

eabd0fed64ef8ef597ac3fe222807feb2dda688326695a2fd1a94807e2e3ad21

Transactions (3)

Coinbase09f37e22f3378c…cf87f6f45e4692

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

87295b311a7170…0e2aa71355dea6

1 in → 2 out247.9404 XPM226 B

Ac8aSJNh…4BAqsrM6 AZrD88Gw…VfzXw8Ei

7b37b3b188e689…511797a39c887f

1 in → 2 out6.1291 XPM226 B

AQBZitg7…LxgpvhqV AZMk3iti…SbiJvtZR

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.

1.735 × 10¹⁰³(104-digit number)

17352135343372269721…86710592011223290399

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

1.735 × 10¹⁰³(104-digit number)

17352135343372269721…86710592011223290399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.735 × 10¹⁰³(104-digit number)

17352135343372269721…86710592011223290401

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

3.470 × 10¹⁰³(104-digit number)

34704270686744539442…73421184022446580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.470 × 10¹⁰³(104-digit number)

34704270686744539442…73421184022446580801

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

6.940 × 10¹⁰³(104-digit number)

69408541373489078884…46842368044893161599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.940 × 10¹⁰³(104-digit number)

69408541373489078884…46842368044893161601

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

1.388 × 10¹⁰⁴(105-digit number)

13881708274697815776…93684736089786323199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.388 × 10¹⁰⁴(105-digit number)

13881708274697815776…93684736089786323201

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

2.776 × 10¹⁰⁴(105-digit number)

27763416549395631553…87369472179572646399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.776 × 10¹⁰⁴(105-digit number)

27763416549395631553…87369472179572646401

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 #460,487

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