Block #92,588

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/1/2013, 7:27:16 PM · Difficulty 9.2045 · 6,697,251 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48c4af1572aeb95237acca068bf5b5334953bf0ecf91a044968658c7ecf7652d

View on Chainz ↗

Height

#92,588

Difficulty

9.204469

Transactions

Size

207 B

Version

Bits

09345811

Nonce

58,610

Timestamp

8/1/2013, 7:27:16 PM

Confirmations

6,697,251

Merkle Root

1a42393c875fc908b911f66a5301a4179c9f2a46accc9a19d84440e9239bf5c8

Transactions (1)

Coinbase1a42393c875fc9…4440e9239bf5c8

1 in → 1 out11.7900 XPM109 B

AcBadmkp…GmhL921o

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.

1.192 × 10¹¹³(114-digit number)

11925371572117492850…56434481533074704589

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

1.192 × 10¹¹³(114-digit number)

11925371572117492850…56434481533074704589

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.192 × 10¹¹³(114-digit number)

11925371572117492850…56434481533074704591

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

2.385 × 10¹¹³(114-digit number)

23850743144234985700…12868963066149409179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.385 × 10¹¹³(114-digit number)

23850743144234985700…12868963066149409181

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

4.770 × 10¹¹³(114-digit number)

47701486288469971400…25737926132298818359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.770 × 10¹¹³(114-digit number)

47701486288469971400…25737926132298818361

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

9.540 × 10¹¹³(114-digit number)

95402972576939942801…51475852264597636719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.540 × 10¹¹³(114-digit number)

95402972576939942801…51475852264597636721

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

1.908 × 10¹¹⁴(115-digit number)

19080594515387988560…02951704529195273439

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