Block #426,003

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 7:50:12 AM · Difficulty 10.3591 · 6,383,850 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b83d1c1baa53f6a84b145b9a91794fcb30fc90e01b427d02e33c990b8ea0587c

View on Chainz ↗

Height

#426,003

Difficulty

10.359096

Transactions

Size

1.31 KB

Version

Bits

0a5bedbc

Nonce

813

Timestamp

3/2/2014, 7:50:12 AM

Confirmations

6,383,850

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

297a482c7c30fa8fb2b79de9452e6d31ccbcd75cfc2da121e7dbb56a3c284ff4

Transactions (2)

Coinbase854f481b104c95…ef323ca2d4765d

1 in → 24 out9.3000 XPM879 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

0144d6dab58ee0…f4fc5a0e209725

2 in → 2 out3.9909 XPM374 B

AUhd124z…dSkJekWW ATmRkvGc…BHA5jXn1

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.

1.023 × 10⁹³(94-digit number)

10238378045962897559…86332191002877456639

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

1.023 × 10⁹³(94-digit number)

10238378045962897559…86332191002877456639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.023 × 10⁹³(94-digit number)

10238378045962897559…86332191002877456641

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

2.047 × 10⁹³(94-digit number)

20476756091925795118…72664382005754913279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.047 × 10⁹³(94-digit number)

20476756091925795118…72664382005754913281

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

4.095 × 10⁹³(94-digit number)

40953512183851590236…45328764011509826559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.095 × 10⁹³(94-digit number)

40953512183851590236…45328764011509826561

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

8.190 × 10⁹³(94-digit number)

81907024367703180473…90657528023019653119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.190 × 10⁹³(94-digit number)

81907024367703180473…90657528023019653121

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

1.638 × 10⁹⁴(95-digit number)

16381404873540636094…81315056046039306239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.638 × 10⁹⁴(95-digit number)

16381404873540636094…81315056046039306241

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 #426,003

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