Block #457,906

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 5:29:15 AM · Difficulty 10.4212 · 6,344,646 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ebca72bf1646e3b985b9cd72bb918306e5718dc1ee8d6cf6fd6f699d37a21818

View on Chainz ↗

Height

#457,906

Difficulty

10.421227

Transactions

Size

3.26 KB

Version

Bits

0a6bd587

Nonce

8,928,395

Timestamp

3/24/2014, 5:29:15 AM

Confirmations

6,344,646

Mined by

⛏️ P2SHAJe8kn69uFa9tzPxDVw3d85cHbpHR32bCr

Merkle Root

bcb6ed0fd2070970db4d6b1db7bda2bdec76255a2b93543e99fac1e82f5f8d22

Transactions (5)

Coinbase4509300e59e089…649854887147e6

1 in → 1 out9.2433 XPM109 B

AJe8kn69…pHR32bCr

5dd709730b72c8…5e7c1e517f6fb3

4 in → 2 out1.9879 XPM668 B

AcSub6rU…2zDLojV5 AQjvW3VG…kqKeQURR

beb9c56cb17342…a0ff22ea217201

9 in → 1 out2.3000 XPM1.34 KB

AQs3gkvJ…cQrJj6vD

f5529e23c36f98…7a42b924e0cf1f

2 in → 5 out11.5416 XPM476 B

AS4CfFYA…ksiezrwM AQhMzWVC…wfpJe2JS AdPYnVrm…VPr3HEKX ATfne49g…EMbPLKn4 ALuGzvqA…evneZf4i

53001cbf243e3c…d1fcf720913edc

3 in → 5 out11.5098 XPM623 B

AS4CfFYA…ksiezrwM AQhMzWVC…wfpJe2JS AdPYnVrm…VPr3HEKX AX2tT8XU…GXBNNbpH ATfne49g…EMbPLKn4

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.

2.125 × 10⁹⁴(95-digit number)

21257800255099511815…52515590215652571839

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

2.125 × 10⁹⁴(95-digit number)

21257800255099511815…52515590215652571839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.125 × 10⁹⁴(95-digit number)

21257800255099511815…52515590215652571841

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

4.251 × 10⁹⁴(95-digit number)

42515600510199023630…05031180431305143679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.251 × 10⁹⁴(95-digit number)

42515600510199023630…05031180431305143681

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

8.503 × 10⁹⁴(95-digit number)

85031201020398047260…10062360862610287359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.503 × 10⁹⁴(95-digit number)

85031201020398047260…10062360862610287361

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

1.700 × 10⁹⁵(96-digit number)

17006240204079609452…20124721725220574719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.700 × 10⁹⁵(96-digit number)

17006240204079609452…20124721725220574721

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

3.401 × 10⁹⁵(96-digit number)

34012480408159218904…40249443450441149439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.401 × 10⁹⁵(96-digit number)

34012480408159218904…40249443450441149441

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