Block #460,589

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 3:30:58 AM · Difficulty 10.4147 · 6,354,548 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a422d02b3a0b041c4f1afc08ed27e9ce91db6d762aa1ac8fb5ea036450046e2

View on Chainz ↗

Height

#460,589

Difficulty

10.414732

Transactions

Size

1.45 KB

Version

Bits

0a6a2be2

Nonce

643,781

Timestamp

3/26/2014, 3:30:58 AM

Confirmations

6,354,548

Mined by

⛏️ P2SHAVkvQmUFnw9Evo2yZnjF7h2WWruQBnxTvL

Merkle Root

33baa660053c595be8fa3aa68a96d3e63f9fa51db67338b61398b089f45ce972

Transactions (3)

Coinbaseada832aa5496de…efa68e471851d7

1 in → 1 out9.2400 XPM109 B

AVkvQmUF…uQBnxTvL

0ef35a4cf6fe2a…6a5e58b4610d44

5 in → 13 out38.5942 XPM1.03 KB

AKvmkWxd…MSDJswJr APvZTPuQ…m4bzSnZ3 AWjbJ2on…vc84xGe1 AXsfZjZQ…YYKTGnTt AJKL4q8d…XtzHGUqD

7374c3e796b96f…6aff216e65a264

1 in → 2 out1.2150 XPM226 B

AGsvjvAk…GyN75LsX AW34SnJH…ATu9ZQEU

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.

7.565 × 10¹⁰¹(102-digit number)

75658176742882511250…54678074815098222579

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

7.565 × 10¹⁰¹(102-digit number)

75658176742882511250…54678074815098222579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.565 × 10¹⁰¹(102-digit number)

75658176742882511250…54678074815098222581

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

1.513 × 10¹⁰²(103-digit number)

15131635348576502250…09356149630196445159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.513 × 10¹⁰²(103-digit number)

15131635348576502250…09356149630196445161

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

3.026 × 10¹⁰²(103-digit number)

30263270697153004500…18712299260392890319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.026 × 10¹⁰²(103-digit number)

30263270697153004500…18712299260392890321

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

6.052 × 10¹⁰²(103-digit number)

60526541394306009000…37424598520785780639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.052 × 10¹⁰²(103-digit number)

60526541394306009000…37424598520785780641

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

1.210 × 10¹⁰³(104-digit number)

12105308278861201800…74849197041571561279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.210 × 10¹⁰³(104-digit number)

12105308278861201800…74849197041571561281

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 #460,589

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