Block #82,755

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 3:34:48 PM · Difficulty 9.2760 · 6,708,185 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d66dcf9e6fbba51c557a88545374727caa3408f74b02599f135207d701517a6

View on Chainz ↗

Height

#82,755

Difficulty

9.276013

Transactions

Size

1.43 KB

Version

Bits

0946a8ca

Nonce

86,833

Timestamp

7/25/2013, 3:34:48 PM

Confirmations

6,708,185

Merkle Root

bccd2cae7ec0c7ff60af70841983445261e008dcff780d6571aedd85d9041699

Transactions (2)

Coinbase33c30e7bec0f39…7813a81c0e09bb

1 in → 1 out11.6300 XPM109 B

AHGi8wDB…eKomrPdd

d448ac173461cb…6c2ec670df6858

10 in → 1 out98.3200 XPM1.23 KB

AT3efowp…sgm6DVMF

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.

1.146 × 10¹¹³(114-digit number)

11468475975703383760…08951069181699943659

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

1.146 × 10¹¹³(114-digit number)

11468475975703383760…08951069181699943659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.146 × 10¹¹³(114-digit number)

11468475975703383760…08951069181699943661

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

2.293 × 10¹¹³(114-digit number)

22936951951406767521…17902138363399887319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.293 × 10¹¹³(114-digit number)

22936951951406767521…17902138363399887321

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

4.587 × 10¹¹³(114-digit number)

45873903902813535043…35804276726799774639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.587 × 10¹¹³(114-digit number)

45873903902813535043…35804276726799774641

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

9.174 × 10¹¹³(114-digit number)

91747807805627070086…71608553453599549279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.174 × 10¹¹³(114-digit number)

91747807805627070086…71608553453599549281

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

1.834 × 10¹¹⁴(115-digit number)

18349561561125414017…43217106907199098559

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