Block #460,578

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 3:11:29 AM · Difficulty 10.4159 · 6,366,564 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70d3bd37a0a0fd1a31bde6a9d0d7a36a89db7404b670a65548318dccede24682

View on Chainz ↗

Height

#460,578

Difficulty

10.415887

Transactions

Size

1.51 KB

Version

Bits

0a6a7792

Nonce

46,924,776

Timestamp

3/26/2014, 3:11:29 AM

Confirmations

6,366,564

Mined by

⛏️ P2SHALCx3p31jnSxaVQkdA7JjkSu7WSqvNtEqE

Merkle Root

da1e0e7585d32d064e154a88cecc30838e561971e4d1d30d8dcd78e4ab088bd0

Transactions (5)

Coinbaseff37e43ecb5160…bd1c8228fc4e72

1 in → 1 out9.2400 XPM110 B

ALCx3p31…SqvNtEqE

23757781adf782…1376754aa46e35

3 in → 2 out257.4029 XPM521 B

AHnNDJxn…3TvsDy71 AYv8jTbs…Mok7Kz9e

558c667e3f6606…f445b395a568f7

1 in → 2 out8.8723 XPM225 B

ANSb5hnU…vw67F4BT AeicsUfV…H1kjrBjV

fd0b2ce6a4dda4…7afb849c7d9f22

1 in → 2 out72.7493 XPM226 B

AYxev7Pm…8SjAybcf ATvUtZYY…3GWzc7aS

87ac12ba6dcb7d…ed339ff60b1354

2 in → 2 out44.4983 XPM372 B

Ab6kpP1V…MYf9b7AA AYxev7Pm…8SjAybcf

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.

8.887 × 10⁹⁵(96-digit number)

88878469771949416473…30471321555302083199

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

8.887 × 10⁹⁵(96-digit number)

88878469771949416473…30471321555302083199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.887 × 10⁹⁵(96-digit number)

88878469771949416473…30471321555302083201

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

1.777 × 10⁹⁶(97-digit number)

17775693954389883294…60942643110604166399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.777 × 10⁹⁶(97-digit number)

17775693954389883294…60942643110604166401

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

3.555 × 10⁹⁶(97-digit number)

35551387908779766589…21885286221208332799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.555 × 10⁹⁶(97-digit number)

35551387908779766589…21885286221208332801

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

7.110 × 10⁹⁶(97-digit number)

71102775817559533178…43770572442416665599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.110 × 10⁹⁶(97-digit number)

71102775817559533178…43770572442416665601

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

1.422 × 10⁹⁷(98-digit number)

14220555163511906635…87541144884833331199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.422 × 10⁹⁷(98-digit number)

14220555163511906635…87541144884833331201

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 #460,578

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