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Block #254,228

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 2:35:10 PM · Difficulty 9.9729 · 6,572,312 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1b06143104bb959cf44fcb8c413729596573afc989acc815ca4aba3af6a9614

View on Chainz ↗

Height

#254,228

Difficulty

9.972937

Transactions

Size

1.48 KB

Version

Bits

09f9126d

Nonce

107,300

Timestamp

11/10/2013, 2:35:10 PM

Confirmations

6,572,312

Merkle Root

50d03c30ffca26f1cc3df6d4d8bc9b5f8669b0ae01839d0796477fd10cb9ed13

Transactions (1)

Coinbase50d03c30ffca26…477fd10cb9ed13

1 in → 40 out10.0195 XPM1.39 KB

AJaGRnaj…iCHGoy6E AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5 AMdvB6BS…DPq9FYdA AWsge36A…wTk5iPiH

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.

4.624 × 10⁹⁴(95-digit number)

46240635491331265432…34322774371316418560

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

4.624 × 10⁹⁴(95-digit number)

46240635491331265432…34322774371316418559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.624 × 10⁹⁴(95-digit number)

46240635491331265432…34322774371316418561

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

9.248 × 10⁹⁴(95-digit number)

92481270982662530864…68645548742632837119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.248 × 10⁹⁴(95-digit number)

92481270982662530864…68645548742632837121

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

1.849 × 10⁹⁵(96-digit number)

18496254196532506172…37291097485265674239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.849 × 10⁹⁵(96-digit number)

18496254196532506172…37291097485265674241

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

3.699 × 10⁹⁵(96-digit number)

36992508393065012345…74582194970531348479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.699 × 10⁹⁵(96-digit number)

36992508393065012345…74582194970531348481

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

7.398 × 10⁹⁵(96-digit number)

73985016786130024691…49164389941062696959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.398 × 10⁹⁵(96-digit number)

73985016786130024691…49164389941062696961

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 254228

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock c1b06143104bb959cf44fcb8c413729596573afc989acc815ca4aba3af6a9614

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #254,228 on Chainz ↗

Block #254,228

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