Block #256,328

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 6:34:19 PM · Difficulty 9.9752 · 6,535,155 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bdf41a931b726057fad3ed05867195baec60452b6b77a4bc8566c92578f59e7d

View on Chainz ↗

Height

#256,328

Difficulty

9.975170

Transactions

Size

1.08 KB

Version

Bits

09f9a4b9

Nonce

24,325

Timestamp

11/11/2013, 6:34:19 PM

Confirmations

6,535,155

Merkle Root

8c060b16e540f82d0d56471543151f3dd8f6948fa70314c17d00e19ebfdc56ef

Transactions (5)

Coinbaseeacf6502507af7…94ff6668236c92

1 in → 2 out10.0700 XPM141 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

8ab6ea360d5cc3…0d738ead98967d

1 in → 1 out3.0179 XPM192 B

AZekc9vM…TkyD7EeC

335e39bb73d2ae…b6216bc2e982d2

1 in → 2 out8.0148 XPM226 B

AbRvbBhR…nE1kogRe AaVFHFSq…bCnX1Bpw

327a6f1db133b5…e807e2980c803a

1 in → 2 out0.9900 XPM225 B

ASUJFtQT…Cqr8nBVx AXfHhb3s…jPzesMRx

cc7f8c2740314d…674f9fc277cec8

1 in → 2 out3.9168 XPM226 B

ASnSjgQg…fewAaNPL ALqgjPPE…ZBSJugya

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.

1.056 × 10⁹⁶(97-digit number)

10568776060024475470…58507442459449571809

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

1.056 × 10⁹⁶(97-digit number)

10568776060024475470…58507442459449571809

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.056 × 10⁹⁶(97-digit number)

10568776060024475470…58507442459449571811

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

2.113 × 10⁹⁶(97-digit number)

21137552120048950941…17014884918899143619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.113 × 10⁹⁶(97-digit number)

21137552120048950941…17014884918899143621

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

4.227 × 10⁹⁶(97-digit number)

42275104240097901882…34029769837798287239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.227 × 10⁹⁶(97-digit number)

42275104240097901882…34029769837798287241

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

8.455 × 10⁹⁶(97-digit number)

84550208480195803765…68059539675596574479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.455 × 10⁹⁶(97-digit number)

84550208480195803765…68059539675596574481

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

1.691 × 10⁹⁷(98-digit number)

16910041696039160753…36119079351193148959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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