Block #126,589

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/20/2013, 11:48:01 PM · Difficulty 9.7810 · 6,663,244 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5927f161bd55dc75482bb6748784453917c48966f13788af8a0cada6fa3474b4

View on Chainz ↗

Height

#126,589

Difficulty

9.781009

Transactions

Size

2.66 KB

Version

Bits

09c7f039

Nonce

29,371

Timestamp

8/20/2013, 11:48:01 PM

Confirmations

6,663,244

Merkle Root

38e51a36d23eb5448bd851d4a08050ac46ea68e0206abbc89524320874fa9b81

Transactions (5)

Coinbase58cc71556a00a3…b8f7bc4b41c9d6

1 in → 1 out10.4900 XPM109 B

AKvnYqzV…YStNr4s5

aeab65e3bcb1c9…e91a8bd83b0ee7

1 in → 1 out199.9900 XPM193 B

AFqDj4vn…D3w8GBCw

cab2a5f6539b92…c4dcb7e06f2a7f

4 in → 1 out42.0000 XPM499 B

ATWpCFic…6AT1WprT

cddabd17b7da4b…22c24976f14ae8

14 in → 2 out147.0300 XPM1.63 KB

AZ1EJ7k6…k5uL1fHg ATWpCFic…6AT1WprT

0b7f7d39de3e76…186e01b35b7058

1 in → 1 out10.4800 XPM158 B

AeTde7fH…w7crTzqr

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.

4.447 × 10¹⁰⁵(106-digit number)

44479981619273198725…32856389193342797359

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

4.447 × 10¹⁰⁵(106-digit number)

44479981619273198725…32856389193342797359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.447 × 10¹⁰⁵(106-digit number)

44479981619273198725…32856389193342797361

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

8.895 × 10¹⁰⁵(106-digit number)

88959963238546397450…65712778386685594719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.895 × 10¹⁰⁵(106-digit number)

88959963238546397450…65712778386685594721

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

1.779 × 10¹⁰⁶(107-digit number)

17791992647709279490…31425556773371189439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.779 × 10¹⁰⁶(107-digit number)

17791992647709279490…31425556773371189441

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

3.558 × 10¹⁰⁶(107-digit number)

35583985295418558980…62851113546742378879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.558 × 10¹⁰⁶(107-digit number)

35583985295418558980…62851113546742378881

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

7.116 × 10¹⁰⁶(107-digit number)

71167970590837117960…25702227093484757759

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