Block #495,389

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 2:49:23 PM · Difficulty 10.7362 · 6,335,105 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ada316a443e71684924e8d61f0b1d5054be8600f35d949cbb9ed3fa89ecb5751

View on Chainz ↗

Height

#495,389

Difficulty

10.736194

Transactions

Size

579 B

Version

Bits

0abc7732

Nonce

143,013,750

Timestamp

4/16/2014, 2:49:23 PM

Confirmations

6,335,105

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

77736f55d31665946a30c1437afa6e9896543ebc852d6de7697159577fc6dd9f

Transactions (2)

Coinbase9ef70077a422ee…82e2697add633e

1 in → 1 out8.6700 XPM116 B

AbwWkWZt…kawDhufa

045b88e625e1bb…4b85e901051bb4

2 in → 2 out5.1488 XPM372 B

AeifehiF…ZbMKYwqx ALgF9qpp…vgZWtgZQ

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.

8.385 × 10⁹⁷(98-digit number)

83854372386124792242…84818282049208103919

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

8.385 × 10⁹⁷(98-digit number)

83854372386124792242…84818282049208103919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.385 × 10⁹⁷(98-digit number)

83854372386124792242…84818282049208103921

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

1.677 × 10⁹⁸(99-digit number)

16770874477224958448…69636564098416207839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.677 × 10⁹⁸(99-digit number)

16770874477224958448…69636564098416207841

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

3.354 × 10⁹⁸(99-digit number)

33541748954449916897…39273128196832415679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.354 × 10⁹⁸(99-digit number)

33541748954449916897…39273128196832415681

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

6.708 × 10⁹⁸(99-digit number)

67083497908899833794…78546256393664831359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.708 × 10⁹⁸(99-digit number)

67083497908899833794…78546256393664831361

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

1.341 × 10⁹⁹(100-digit number)

13416699581779966758…57092512787329662719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.341 × 10⁹⁹(100-digit number)

13416699581779966758…57092512787329662721

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 #495,389

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