Block #138,457

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/28/2013, 10:05:21 AM · Difficulty 9.8267 · 6,670,137 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6e4687d8e65bc889bd27062003c48c3a6c096f039f39c9fcef5abd2a998cefb

View on Chainz ↗

Height

#138,457

Difficulty

9.826702

Transactions

Size

1018 B

Version

Bits

09d3a2b9

Nonce

190,536

Timestamp

8/28/2013, 10:05:21 AM

Confirmations

6,670,137

Mined by

⛏️ P2SHAZLKVbqD8XNGsuiSXKq7s6gRM3CSGq6Yi3

Merkle Root

61489f41d28224e6a9b133a7c1b535c397be244eb9e4585ba60e7c1ad539bffb

Transactions (2)

Coinbase7da80166241086…d7cdbba4e4fa65

1 in → 1 out10.3500 XPM109 B

AZLKVbqD…CSGq6Yi3

ac3dac1ef0b9cc…f70b8b78d179df

5 in → 2 out219.5819 XPM817 B

AXEJXAHi…LnJS4BKi AYtMiX9E…Q2uYCGgD

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.

2.006 × 10⁹⁸(99-digit number)

20061832717936317590…82886316230409016179

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

2.006 × 10⁹⁸(99-digit number)

20061832717936317590…82886316230409016179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.006 × 10⁹⁸(99-digit number)

20061832717936317590…82886316230409016181

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

4.012 × 10⁹⁸(99-digit number)

40123665435872635181…65772632460818032359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.012 × 10⁹⁸(99-digit number)

40123665435872635181…65772632460818032361

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

8.024 × 10⁹⁸(99-digit number)

80247330871745270363…31545264921636064719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.024 × 10⁹⁸(99-digit number)

80247330871745270363…31545264921636064721

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

1.604 × 10⁹⁹(100-digit number)

16049466174349054072…63090529843272129439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.604 × 10⁹⁹(100-digit number)

16049466174349054072…63090529843272129441

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

3.209 × 10⁹⁹(100-digit number)

32098932348698108145…26181059686544258879

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 #138,457

Cookie Preferences