Block #403,875

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 11:27:02 AM · Difficulty 10.4324 · 6,404,263 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c6d1e1dd95d4fa6f890f69be4a5967f0b9226488c8bb5544b59a7cb7eb3ea97f

View on Chainz ↗

Height

#403,875

Difficulty

10.432407

Transactions

Size

867 B

Version

Bits

0a6eb241

Nonce

18,733

Timestamp

2/14/2014, 11:27:02 AM

Confirmations

6,404,263

Mined by

⛏️ aRPAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

0b8fb20cc39eea822ec7591abe2832d1c284e18f1bf0cba0ad1319b7ccbbaa6c

Transactions (1)

Coinbase0b8fb20cc39eea…1319b7ccbbaa6c

1 in → 21 out9.1700 XPM777 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6

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.

2.482 × 10⁹⁵(96-digit number)

24829097293409911394…34629262910085951999

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

2.482 × 10⁹⁵(96-digit number)

24829097293409911394…34629262910085951999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.482 × 10⁹⁵(96-digit number)

24829097293409911394…34629262910085952001

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

4.965 × 10⁹⁵(96-digit number)

49658194586819822788…69258525820171903999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.965 × 10⁹⁵(96-digit number)

49658194586819822788…69258525820171904001

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

9.931 × 10⁹⁵(96-digit number)

99316389173639645576…38517051640343807999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.931 × 10⁹⁵(96-digit number)

99316389173639645576…38517051640343808001

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

1.986 × 10⁹⁶(97-digit number)

19863277834727929115…77034103280687615999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.986 × 10⁹⁶(97-digit number)

19863277834727929115…77034103280687616001

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

3.972 × 10⁹⁶(97-digit number)

39726555669455858230…54068206561375231999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.972 × 10⁹⁶(97-digit number)

39726555669455858230…54068206561375232001

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 #403,875

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