Block #1,537,925

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2016, 12:36:52 PM · Difficulty 10.6330 · 5,271,744 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a96ea7394095ec84157cc10c89ebf7fb54a09c26b6c80a3b52bd1a34f855e41b

View on Chainz ↗

Height

#1,537,925

Difficulty

10.633005

Transactions

Size

5.74 KB

Version

Bits

0aa20ca1

Nonce

64,720,694

Timestamp

4/12/2016, 12:36:52 PM

Confirmations

5,271,744

Mined by

⛏️ P2SHAekjJLSkCc6UZHGS1P1YbzKmNfJenAM4hW

Merkle Root

c0c72359acf95d6b7a7435075c16a943397fc1d03bcdd6f764419b860c10c2d9

Transactions (4)

Coinbase45f068d63b0194…675ae5edd4e99b

1 in → 1 out8.8900 XPM109 B

AekjJLSk…JenAM4hW

6752d598cb4fda…4372b7350ff082

1 in → 51 out26.7107 XPM1.85 KB

AWJbVgXA…1LTxX4MP AaSmSYsf…MwctnpJC AUAzip4H…EYhdgmXH AFxxYVtW…76zFbjN1 AZ3cZHxS…1qdoLqba

4c05fb1d56d1c4…9a3557280bc9bf

1 in → 51 out2.2782 XPM1.85 KB

AKHb9FgM…MmttZ9gm AcDC1coh…4GRCmUYM ALWcRwqS…KAy9F9nQ ANeyCe88…Np4Tmudi ALPjPA5B…tAd6jwhQ

7427fa7f61cf5d…60b0303bae9cd7

1 in → 51 out2.0128 XPM1.85 KB

AN3aiytD…HfFoV2sJ AHLrfMCb…5eE2yTTn Ac6LdCuN…8KRMHPj7 AQ3uAoVE…gkgEyiPv AQmwGzic…imw8Bix3

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.

9.229 × 10⁹⁴(95-digit number)

92294191360875269701…57807130065096385119

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

9.229 × 10⁹⁴(95-digit number)

92294191360875269701…57807130065096385119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.229 × 10⁹⁴(95-digit number)

92294191360875269701…57807130065096385121

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

1.845 × 10⁹⁵(96-digit number)

18458838272175053940…15614260130192770239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.845 × 10⁹⁵(96-digit number)

18458838272175053940…15614260130192770241

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

3.691 × 10⁹⁵(96-digit number)

36917676544350107880…31228520260385540479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.691 × 10⁹⁵(96-digit number)

36917676544350107880…31228520260385540481

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

7.383 × 10⁹⁵(96-digit number)

73835353088700215761…62457040520771080959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.383 × 10⁹⁵(96-digit number)

73835353088700215761…62457040520771080961

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

1.476 × 10⁹⁶(97-digit number)

14767070617740043152…24914081041542161919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.476 × 10⁹⁶(97-digit number)

14767070617740043152…24914081041542161921

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 #1,537,925

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