Block #241,923

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 11:57:05 AM · Difficulty 9.9587 · 6,561,533 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e3a1023ebf30b1524022e015943051aa4e7080a9effd58d2c9bc1872f8e21a6

View on Chainz ↗

Height

#241,923

Difficulty

9.958731

Transactions

Size

1.64 KB

Version

Bits

09f56f60

Nonce

44,008

Timestamp

11/3/2013, 11:57:05 AM

Confirmations

6,561,533

Mined by

⛏️ Rv7z,AXvKAbupBzH3NDftHGGChE8Y5HbNGDLh39

Merkle Root

c418b768598f991b8adec5d8fff985f416baaca540a54da98bf820d52b099383

Transactions (1)

Coinbasec418b768598f99…f820d52b099383

1 in → 45 out10.0487 XPM1.55 KB

AXvKAbup…bNGDLh39 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AcMPa5Yh…j5yHgkwm Ac5sZcdP…kzV4eckG

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.

8.418 × 10⁹¹(92-digit number)

84183262177288225939…07841593005359717759

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

8.418 × 10⁹¹(92-digit number)

84183262177288225939…07841593005359717759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.418 × 10⁹¹(92-digit number)

84183262177288225939…07841593005359717761

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

1.683 × 10⁹²(93-digit number)

16836652435457645187…15683186010719435519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.683 × 10⁹²(93-digit number)

16836652435457645187…15683186010719435521

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

3.367 × 10⁹²(93-digit number)

33673304870915290375…31366372021438871039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.367 × 10⁹²(93-digit number)

33673304870915290375…31366372021438871041

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

6.734 × 10⁹²(93-digit number)

67346609741830580751…62732744042877742079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.734 × 10⁹²(93-digit number)

67346609741830580751…62732744042877742081

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

1.346 × 10⁹³(94-digit number)

13469321948366116150…25465488085755484159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.346 × 10⁹³(94-digit number)

13469321948366116150…25465488085755484161

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