Block #44,658

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 12:19:34 AM · Difficulty 8.7251 · 6,745,379 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

011fe3427f388caf5333513e7f565b0dc2bcb94bf921c85d50fd84ff2d0b278f

View on Chainz ↗

Height

#44,658

Difficulty

8.725132

Transactions

Size

540 B

Version

Bits

08b9a23f

Nonce

154

Timestamp

7/15/2013, 12:19:34 AM

Confirmations

6,745,379

Merkle Root

28b876fbf48ebec489720934578a814e2b15a2fa38e8b26d832082425a469776

Transactions (2)

Coinbasecc0550d45c7d81…a360f80ed268c1

1 in → 1 out13.1300 XPM110 B

ARXW9nxx…wWS3FZFj

397b477bc48de1…757bbed6fd0cb1

2 in → 1 out29.2600 XPM339 B

AJ5JDkMB…S91bdMiR

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.

3.903 × 10⁹⁶(97-digit number)

39039128463821323546…72575581919450952359

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

3.903 × 10⁹⁶(97-digit number)

39039128463821323546…72575581919450952359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.903 × 10⁹⁶(97-digit number)

39039128463821323546…72575581919450952361

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

7.807 × 10⁹⁶(97-digit number)

78078256927642647092…45151163838901904719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.807 × 10⁹⁶(97-digit number)

78078256927642647092…45151163838901904721

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

1.561 × 10⁹⁷(98-digit number)

15615651385528529418…90302327677803809439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.561 × 10⁹⁷(98-digit number)

15615651385528529418…90302327677803809441

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

3.123 × 10⁹⁷(98-digit number)

31231302771057058837…80604655355607618879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.123 × 10⁹⁷(98-digit number)

31231302771057058837…80604655355607618881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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