Block #253,813

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 9:00:34 AM · Difficulty 9.9725 · 6,541,430 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9675296a24e7f2404b46b1c76dc3d942dda884bb8a506c54701c8543cc2a4d1b

View on Chainz ↗

Height

#253,813

Difficulty

9.972487

Transactions

Size

1.84 KB

Version

Bits

09f8f4ef

Nonce

37,142

Timestamp

11/10/2013, 9:00:34 AM

Confirmations

6,541,430

Mined by

⛏️ uaRKBAGqNUmihx5mYSF5juhEAu2Unf42vwEZE6L

Merkle Root

4bb6138021ef685aba3c1204546b0062a4f69c025199007096045c50f67f1b17

Transactions (1)

Coinbase4bb6138021ef68…045c50f67f1b17

1 in → 51 out10.0200 XPM1.75 KB

AGqNUmih…2vwEZE6L AG9H2B8p…eiaSPdGS AScCYXya…oAz38X3p AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5

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.

4.583 × 10⁹⁴(95-digit number)

45830232391917739304…46711016308317555749

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

4.583 × 10⁹⁴(95-digit number)

45830232391917739304…46711016308317555749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.583 × 10⁹⁴(95-digit number)

45830232391917739304…46711016308317555751

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

9.166 × 10⁹⁴(95-digit number)

91660464783835478609…93422032616635111499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.166 × 10⁹⁴(95-digit number)

91660464783835478609…93422032616635111501

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

1.833 × 10⁹⁵(96-digit number)

18332092956767095721…86844065233270222999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.833 × 10⁹⁵(96-digit number)

18332092956767095721…86844065233270223001

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

3.666 × 10⁹⁵(96-digit number)

36664185913534191443…73688130466540445999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.666 × 10⁹⁵(96-digit number)

36664185913534191443…73688130466540446001

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

7.332 × 10⁹⁵(96-digit number)

73328371827068382887…47376260933080891999

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