Block #508,791

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/24/2014, 3:17:22 PM · Difficulty 10.8188 · 6,333,561 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12f9320841cbd433ef43a8aafdf9f1c9df10ccae1adc3dc0d81ba239247ded1e

View on Chainz ↗

Height

#508,791

Difficulty

10.818823

Transactions

Size

798 B

Version

Bits

0ad19e5a

Nonce

92,849

Timestamp

4/24/2014, 3:17:22 PM

Confirmations

6,333,561

Mined by

⛏️ waSY*ATKK7iFzxU98qfet38JZnUDJ7swZm46KN1

Merkle Root

9edfa61bb480551348f8de29fb16c4f10dc98dadaab1151328e61fdb1f9a355a

Transactions (1)

Coinbase9edfa61bb48055…e61fdb1f9a355a

1 in → 19 out8.5300 XPM709 B

ATKK7iFz…wZm46KN1 AdxPNkWD…ZMa9u34q AQvZBsUo…hppgRZTJ AKQ8tFA9…PtdHk9WH ANNg88pG…ppn21sTe

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.

2.079 × 10⁹²(93-digit number)

20797627164322154583…86666795344986671359

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

2.079 × 10⁹²(93-digit number)

20797627164322154583…86666795344986671359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.079 × 10⁹²(93-digit number)

20797627164322154583…86666795344986671361

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

4.159 × 10⁹²(93-digit number)

41595254328644309167…73333590689973342719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.159 × 10⁹²(93-digit number)

41595254328644309167…73333590689973342721

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

8.319 × 10⁹²(93-digit number)

83190508657288618334…46667181379946685439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.319 × 10⁹²(93-digit number)

83190508657288618334…46667181379946685441

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

1.663 × 10⁹³(94-digit number)

16638101731457723666…93334362759893370879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.663 × 10⁹³(94-digit number)

16638101731457723666…93334362759893370881

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

3.327 × 10⁹³(94-digit number)

33276203462915447333…86668725519786741759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.327 × 10⁹³(94-digit number)

33276203462915447333…86668725519786741761

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 #508,791

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