Block #259,542

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 4:40:55 PM · Difficulty 9.9774 · 6,536,319 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6470c7c0940cf4439a0744f0a3c1287f42a6de8c4919ec8438bb37daf72d8924

View on Chainz ↗

Height

#259,542

Difficulty

9.977380

Transactions

Size

1.91 KB

Version

Bits

09fa3593

Nonce

37,248

Timestamp

11/13/2013, 4:40:55 PM

Confirmations

6,536,319

Mined by

⛏️ aRoAWVGtkZjtmGB9uiXWk5CN7Frmcm321bzSA

Merkle Root

be2c030d6509edc7528bafbeb5db6381ea1fd812f9b581aa4cfb436647a01228

Transactions (1)

Coinbasebe2c030d6509ed…fb436647a01228

1 in → 53 out10.0100 XPM1.82 KB

AWVGtkZj…m321bzSA AKXeSXzu…yeuNjvhB AQtzUSwq…htAuF3yC AGkijaif…KdtGyjTE AeNjg8HA…9AkdpcSC

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.

4.018 × 10⁹³(94-digit number)

40185813331365291720…59343069880288700799

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

4.018 × 10⁹³(94-digit number)

40185813331365291720…59343069880288700799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.018 × 10⁹³(94-digit number)

40185813331365291720…59343069880288700801

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

8.037 × 10⁹³(94-digit number)

80371626662730583441…18686139760577401599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.037 × 10⁹³(94-digit number)

80371626662730583441…18686139760577401601

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

1.607 × 10⁹⁴(95-digit number)

16074325332546116688…37372279521154803199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.607 × 10⁹⁴(95-digit number)

16074325332546116688…37372279521154803201

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

3.214 × 10⁹⁴(95-digit number)

32148650665092233376…74744559042309606399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.214 × 10⁹⁴(95-digit number)

32148650665092233376…74744559042309606401

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

6.429 × 10⁹⁴(95-digit number)

64297301330184466753…49489118084619212799

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