Block #267,662

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 11:16:48 AM · Difficulty 9.9587 · 6,557,033 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9b6d0c1af19beed205931e824c132764b6abe3ea987f78f7605576617adc1d7b

View on Chainz ↗

Height

#267,662

Difficulty

9.958734

Transactions

Size

1.64 KB

Version

Bits

09f56f96

Nonce

10,586

Timestamp

11/21/2013, 11:16:48 AM

Confirmations

6,557,033

Mined by

⛏️ aRe?AKwcMAcHMxC6hzN9c8RsVfpBWrWGekVdtp

Merkle Root

7eccd3af4f425292ae2d4279d3f9eb2fd1a4ecc9cc3fd7051f51bba6a9119fcb

Transactions (1)

Coinbase7eccd3af4f4252…51bba6a9119fcb

1 in → 45 out10.0500 XPM1.56 KB

AKwcMAcH…WGekVdtp AFqKfjez…qX9Ace3g AQyr8Lw3…hs4nt3Pn AdnG9gQ7…N9B7mA2p AK61Jfjk…fenNk1MA

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.

1.244 × 10⁹⁶(97-digit number)

12446326011862664908…11003058530523750399

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

1.244 × 10⁹⁶(97-digit number)

12446326011862664908…11003058530523750399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.244 × 10⁹⁶(97-digit number)

12446326011862664908…11003058530523750401

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

2.489 × 10⁹⁶(97-digit number)

24892652023725329817…22006117061047500799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.489 × 10⁹⁶(97-digit number)

24892652023725329817…22006117061047500801

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

4.978 × 10⁹⁶(97-digit number)

49785304047450659635…44012234122095001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.978 × 10⁹⁶(97-digit number)

49785304047450659635…44012234122095001601

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

9.957 × 10⁹⁶(97-digit number)

99570608094901319270…88024468244190003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.957 × 10⁹⁶(97-digit number)

99570608094901319270…88024468244190003201

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

1.991 × 10⁹⁷(98-digit number)

19914121618980263854…76048936488380006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.991 × 10⁹⁷(98-digit number)

19914121618980263854…76048936488380006401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #267,662

Cookie Preferences