Block #514,354

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2014, 2:50:17 AM · Difficulty 10.8379 · 6,300,114 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07e15b4357656faf894592276087a8fc337631bcc9603528822b84e90d3739f2

View on Chainz ↗

Height

#514,354

Difficulty

10.837884

Transactions

Size

1.59 KB

Version

Bits

0ad67f8b

Nonce

337,226

Timestamp

4/28/2014, 2:50:17 AM

Confirmations

6,300,114

Mined by

⛏️ 2aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

fbb2a61d11c2958e70bcf992fc40d2e954232920c85b194fbeaee1002003ddd9

Transactions (4)

Coinbase4a2afbd61ba120…b8ccf68c65dec7

1 in → 19 out8.5000 XPM709 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AUbecsVa…i8zo8qRf ATKK7iFz…wZm46KN1

723c8b58fcef17…6c332e0460f0de

2 in → 2 out14.3533 XPM374 B

ATDzT9Qg…xPgwgjb1 AMF4rFis…1HGqnF83

7fa61854284fdd…a3d30f6948de4b

1 in → 2 out7.0289 XPM226 B

AYYwATFQ…jS1va8nr AY5fqZ1q…LSHEnHss

ae80c970032ef7…0579812fb7e1cb

1 in → 2 out7.0249 XPM226 B

AUHsZni5…YpdPCyYZ AWMyuS4g…ovqKaCc1

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.

1.195 × 10⁹³(94-digit number)

11951632192499783912…54779784929063365439

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

1.195 × 10⁹³(94-digit number)

11951632192499783912…54779784929063365439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.195 × 10⁹³(94-digit number)

11951632192499783912…54779784929063365441

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

2.390 × 10⁹³(94-digit number)

23903264384999567824…09559569858126730879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.390 × 10⁹³(94-digit number)

23903264384999567824…09559569858126730881

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

4.780 × 10⁹³(94-digit number)

47806528769999135648…19119139716253461759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.780 × 10⁹³(94-digit number)

47806528769999135648…19119139716253461761

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

9.561 × 10⁹³(94-digit number)

95613057539998271296…38238279432506923519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.561 × 10⁹³(94-digit number)

95613057539998271296…38238279432506923521

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

1.912 × 10⁹⁴(95-digit number)

19122611507999654259…76476558865013847039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.912 × 10⁹⁴(95-digit number)

19122611507999654259…76476558865013847041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.824 × 10⁹⁴(95-digit number)

38245223015999308518…52953117730027694079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #514,354

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