Block #275,521

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 6:00:30 PM · Difficulty 9.9610 · 6,531,036 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2b529b85e567093cb30546fb1ce7feee971d5cd270ade4fe62148250f212f6c

View on Chainz ↗

Height

#275,521

Difficulty

9.961007

Transactions

Size

1.42 KB

Version

Bits

09f60495

Nonce

96,361

Timestamp

11/26/2013, 6:00:30 PM

Confirmations

6,531,036

Mined by

⛏️ A4aR>AUQHP8oJt86VFDSokqvtbhV1KhLpEKyRph

Merkle Root

5f289a665a74866ce5e7dad2df043ac7844b785a6289033b808a3552b77e2379

Transactions (2)

Coinbase51bad0a09a4086…498d5233151e1c

1 in → 23 out10.0600 XPM845 B

AUQHP8oJ…LpEKyRph AecDVaur…cBNWBabH AGQxR1oS…2N1xAZXN ARGnYsSp…RHnSamsf AWCkoGXK…zjpfLbCF

5463853f953a6f…3cb63075a6db06

3 in → 2 out6.0125 XPM522 B

ASBTgcNH…zHtLetKn AVVktu9A…gEaoLL6G

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.

2.312 × 10⁹⁸(99-digit number)

23120360576771739482…35446477974756832639

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

2.312 × 10⁹⁸(99-digit number)

23120360576771739482…35446477974756832639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.312 × 10⁹⁸(99-digit number)

23120360576771739482…35446477974756832641

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

4.624 × 10⁹⁸(99-digit number)

46240721153543478965…70892955949513665279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.624 × 10⁹⁸(99-digit number)

46240721153543478965…70892955949513665281

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

9.248 × 10⁹⁸(99-digit number)

92481442307086957931…41785911899027330559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.248 × 10⁹⁸(99-digit number)

92481442307086957931…41785911899027330561

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

1.849 × 10⁹⁹(100-digit number)

18496288461417391586…83571823798054661119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.849 × 10⁹⁹(100-digit number)

18496288461417391586…83571823798054661121

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

3.699 × 10⁹⁹(100-digit number)

36992576922834783172…67143647596109322239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.699 × 10⁹⁹(100-digit number)

36992576922834783172…67143647596109322241

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 #275,521

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