Block #513,830

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2014, 6:46:57 PM · Difficulty 10.8365 · 6,289,961 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

13ba4e7ab1e5213fcc3c452f8604f4280ac1b0e33ed9c96f4d79d1567f40cd45

View on Chainz ↗

Height

#513,830

Difficulty

10.836508

Transactions

Size

765 B

Version

Bits

0ad62569

Nonce

7,376

Timestamp

4/27/2014, 6:46:57 PM

Confirmations

6,289,961

Mined by

⛏️ &aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3a4ed09900a00842f7fcda9c519f6af6e6fb7be2159dee2d45a516b6235419f6

Transactions (1)

Coinbase3a4ed09900a008…a516b6235419f6

1 in → 18 out8.5000 XPM675 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AUbecsVa…i8zo8qRf ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j

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.

2.037 × 10⁹⁵(96-digit number)

20373257625333349900…78026534619056570239

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

2.037 × 10⁹⁵(96-digit number)

20373257625333349900…78026534619056570239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.037 × 10⁹⁵(96-digit number)

20373257625333349900…78026534619056570241

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

4.074 × 10⁹⁵(96-digit number)

40746515250666699800…56053069238113140479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.074 × 10⁹⁵(96-digit number)

40746515250666699800…56053069238113140481

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

8.149 × 10⁹⁵(96-digit number)

81493030501333399601…12106138476226280959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.149 × 10⁹⁵(96-digit number)

81493030501333399601…12106138476226280961

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

1.629 × 10⁹⁶(97-digit number)

16298606100266679920…24212276952452561919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.629 × 10⁹⁶(97-digit number)

16298606100266679920…24212276952452561921

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

3.259 × 10⁹⁶(97-digit number)

32597212200533359840…48424553904905123839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.259 × 10⁹⁶(97-digit number)

32597212200533359840…48424553904905123841

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