Block #134,371

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 12:33:56 AM · Difficulty 9.8034 · 6,656,627 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

66b8b36478ea9289254b70df5204b7377d62fe4e66ae6923d35b4021ca83839a

View on Chainz ↗

Height

#134,371

Difficulty

9.803447

Transactions

Size

661 B

Version

Bits

09cdaead

Nonce

365,132

Timestamp

8/26/2013, 12:33:56 AM

Confirmations

6,656,627

Merkle Root

dc245306a1590c5d9ca7e69008718c1acdc4dd2c88ad77579244c12c54a287fa

Transactions (3)

Coinbase8b75dd649e2ec4…d9a4b60a7b4bd0

1 in → 1 out10.4100 XPM109 B

AX34fYYB…MfbcKm6V

8203ddb973a6e2…85197b7e4baa76

1 in → 1 out99.9900 XPM192 B

AY682pCc…b1Yc5EUZ

74c51354a6fa7e…e97866c830815c

2 in → 1 out20.9200 XPM272 B

AXjdAEmF…6ohvdeSw

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.

1.144 × 10⁹¹(92-digit number)

11444771411318414702…54875643256657108479

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

1.144 × 10⁹¹(92-digit number)

11444771411318414702…54875643256657108479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.144 × 10⁹¹(92-digit number)

11444771411318414702…54875643256657108481

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

2.288 × 10⁹¹(92-digit number)

22889542822636829405…09751286513314216959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.288 × 10⁹¹(92-digit number)

22889542822636829405…09751286513314216961

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

4.577 × 10⁹¹(92-digit number)

45779085645273658811…19502573026628433919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.577 × 10⁹¹(92-digit number)

45779085645273658811…19502573026628433921

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

9.155 × 10⁹¹(92-digit number)

91558171290547317622…39005146053256867839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.155 × 10⁹¹(92-digit number)

91558171290547317622…39005146053256867841

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

1.831 × 10⁹²(93-digit number)

18311634258109463524…78010292106513735679

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