Block #265,423

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 1:27:11 PM · Difficulty 9.9626 · 6,540,791 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9586f8c313b908a77c3272bdc30072f33035d701d67defe5be964911c7b82600

View on Chainz ↗

Height

#265,423

Difficulty

9.962617

Transactions

Size

2.14 KB

Version

Bits

09f66e0b

Nonce

9,074

Timestamp

11/19/2013, 1:27:11 PM

Confirmations

6,540,791

Mined by

⛏️ aRg3AKWzAUKc3CbwP8g7QK3LN9KbmHim8rhc8E

Merkle Root

6fad8b5fc9c2ce54cc2d486065578cff0cb772529c97ef73ad1abad937a7ce7d

Transactions (1)

Coinbase6fad8b5fc9c2ce…1abad937a7ce7d

1 in → 60 out10.0300 XPM2.05 KB

AKWzAUKc…im8rhc8E AFqKfjez…qX9Ace3g AdnG9gQ7…N9B7mA2p AQapNBe8…Pxk4vkev APZy8y6E…QZaGQjfp

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.

1.641 × 10⁹⁶(97-digit number)

16417311301262111457…54986714600264232959

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

1.641 × 10⁹⁶(97-digit number)

16417311301262111457…54986714600264232959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.641 × 10⁹⁶(97-digit number)

16417311301262111457…54986714600264232961

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

3.283 × 10⁹⁶(97-digit number)

32834622602524222914…09973429200528465919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.283 × 10⁹⁶(97-digit number)

32834622602524222914…09973429200528465921

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

6.566 × 10⁹⁶(97-digit number)

65669245205048445828…19946858401056931839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.566 × 10⁹⁶(97-digit number)

65669245205048445828…19946858401056931841

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

1.313 × 10⁹⁷(98-digit number)

13133849041009689165…39893716802113863679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.313 × 10⁹⁷(98-digit number)

13133849041009689165…39893716802113863681

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

2.626 × 10⁹⁷(98-digit number)

26267698082019378331…79787433604227727359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.626 × 10⁹⁷(98-digit number)

26267698082019378331…79787433604227727361

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