Block #458,697

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 6:49:11 PM · Difficulty 10.4211 · 6,350,994 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0b32e30fa577f0137aaad93a36ee7467f52ef34e28ff9bf3590fd95a4d7f2b10

View on Chainz ↗

Height

#458,697

Difficulty

10.421057

Transactions

Size

3.61 KB

Version

Bits

0a6bca6c

Nonce

1,416,619

Timestamp

3/24/2014, 6:49:11 PM

Confirmations

6,350,994

Mined by

⛏️ P2SHASS4VkgCpsWxpkB4LUumvXPVrLv7hXRQta

Merkle Root

469e70ce5e0c51869c5934aa204c5497df33ca0bd35d3b95cc9ff23ad59065b4

Transactions (5)

Coinbasebc7ded9964c1dd…62dfd98346c963

1 in → 1 out9.2500 XPM109 B

ASS4VkgC…v7hXRQta

ed96156e2fb6e2…3ba1a06862548b

1 in → 3 out9.2000 XPM226 B

ARFZrT5B…1x7xwjfW AeKNrjNj…1NEq95Ta AMw6Dcr2…pMu8K6Zs

a0250a273cea94…27eefe166908e5

14 in → 1 out13.9948 XPM2.07 KB

AZHN62B2…uVr5M7LL

84e962aabf6612…fcba263d13562f

6 in → 1 out1.2680 XPM931 B

AUZU6arw…fD7fvxfL

6ddad390d9c5ef…96effaf5e0eccd

1 in → 2 out1.2580 XPM225 B

AJEwbg1o…4bxvzQV4 AcZnQrcp…4Ax2xF4G

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.

1.601 × 10⁹⁶(97-digit number)

16011379311762343737…30482841131933998079

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

1.601 × 10⁹⁶(97-digit number)

16011379311762343737…30482841131933998079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.601 × 10⁹⁶(97-digit number)

16011379311762343737…30482841131933998081

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

3.202 × 10⁹⁶(97-digit number)

32022758623524687474…60965682263867996159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.202 × 10⁹⁶(97-digit number)

32022758623524687474…60965682263867996161

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

6.404 × 10⁹⁶(97-digit number)

64045517247049374948…21931364527735992319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.404 × 10⁹⁶(97-digit number)

64045517247049374948…21931364527735992321

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

1.280 × 10⁹⁷(98-digit number)

12809103449409874989…43862729055471984639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.280 × 10⁹⁷(98-digit number)

12809103449409874989…43862729055471984641

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

2.561 × 10⁹⁷(98-digit number)

25618206898819749979…87725458110943969279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.561 × 10⁹⁷(98-digit number)

25618206898819749979…87725458110943969281

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 #458,697

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