Block #142,724

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/31/2013, 3:40:46 AM · Difficulty 9.8380 · 6,669,589 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

74d85e03aa4632ac48872799c719e3c0709af929466d7f347b6dcb85cfdff8b1

View on Chainz ↗

Height

#142,724

Difficulty

9.837964

Transactions

Size

6.58 KB

Version

Bits

09d684ca

Nonce

139,866

Timestamp

8/31/2013, 3:40:46 AM

Confirmations

6,669,589

Mined by

⛏️ P2SHAUe4mesD3iPwwK1ux2w3dj6nG1UUcueSVP

Merkle Root

06f8f29d06e57213406f030e360424b43fb20bbdec2b1955936d18677cb79265

Transactions (2)

Coinbaseceb5ce6204611f…cf98e43014930b

1 in → 1 out10.3900 XPM109 B

AUe4mesD…UUcueSVP

db90adc1af39c8…c1c6c9cb6a81e0

56 in → 2 out1078.1100 XPM6.38 KB

AQA1JPfd…iiEp6oz3 AQg7hqqd…y1MAuYam

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.

3.073 × 10⁹⁴(95-digit number)

30733188720480269782…41667148832230719999

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

3.073 × 10⁹⁴(95-digit number)

30733188720480269782…41667148832230719999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.073 × 10⁹⁴(95-digit number)

30733188720480269782…41667148832230720001

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

6.146 × 10⁹⁴(95-digit number)

61466377440960539564…83334297664461439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.146 × 10⁹⁴(95-digit number)

61466377440960539564…83334297664461440001

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

1.229 × 10⁹⁵(96-digit number)

12293275488192107912…66668595328922879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.229 × 10⁹⁵(96-digit number)

12293275488192107912…66668595328922880001

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

2.458 × 10⁹⁵(96-digit number)

24586550976384215825…33337190657845759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.458 × 10⁹⁵(96-digit number)

24586550976384215825…33337190657845760001

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

4.917 × 10⁹⁵(96-digit number)

49173101952768431651…66674381315691519999

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

Block #142,724

Cookie Preferences