Block #326,933

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 4:39:04 AM · Difficulty 10.1802 · 6,467,185 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fdfb15529f6dcc7866b8a88a1ca92a96977901979527f9e70524b57d037fe6c1

View on Chainz ↗

Height

#326,933

Difficulty

10.180199

Transactions

Size

572 B

Version

Bits

0a2e217e

Nonce

227,154

Timestamp

12/24/2013, 4:39:04 AM

Confirmations

6,467,185

Merkle Root

fbfe37a4ff139de442e32c683fa7151ff0a9bf8d83572b38e9715758235e065e

Transactions (2)

Coinbase09f2d7ee6a5219…077acf2c704c75

1 in → 1 out9.6400 XPM109 B

AWT4FajA…7qUxCsaJ

1e642a38d91c43…a359c0aa6f9dad

2 in → 2 out1.0650 XPM373 B

AbLbrG11…qiWufZ9e AUeimGLg…QVxJvmnx

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.

8.094 × 10⁹⁵(96-digit number)

80944577044718820802…66633754236975544959

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

8.094 × 10⁹⁵(96-digit number)

80944577044718820802…66633754236975544959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.094 × 10⁹⁵(96-digit number)

80944577044718820802…66633754236975544961

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

1.618 × 10⁹⁶(97-digit number)

16188915408943764160…33267508473951089919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.618 × 10⁹⁶(97-digit number)

16188915408943764160…33267508473951089921

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

3.237 × 10⁹⁶(97-digit number)

32377830817887528321…66535016947902179839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.237 × 10⁹⁶(97-digit number)

32377830817887528321…66535016947902179841

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

6.475 × 10⁹⁶(97-digit number)

64755661635775056642…33070033895804359679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.475 × 10⁹⁶(97-digit number)

64755661635775056642…33070033895804359681

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

1.295 × 10⁹⁷(98-digit number)

12951132327155011328…66140067791608719359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.295 × 10⁹⁷(98-digit number)

12951132327155011328…66140067791608719361

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