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Block #185,545

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 9:14:53 AM · Difficulty 9.8623 · 6,614,814 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

83e53e0b2d76dcd11c5dceb21e2c4bf5657ea11b4ca9d452e188cba9e35f81d6

View on Chainz ↗

Height

#185,545

Difficulty

9.862327

Transactions

Size

651 B

Version

Bits

09dcc16f

Nonce

35,661

Timestamp

9/29/2013, 9:14:53 AM

Confirmations

6,614,814

Merkle Root

d93d942ee3efda246238a76cf62bf8ca11e5387381728e648ae827bee8552611

Transactions (3)

Coinbase90b08bfffc8604…ccc30711a9397a

1 in → 1 out10.2900 XPM109 B

AbtRurUb…ccoN5RXo

aae4240c4a12d8…36da1643c5be7c

1 in → 2 out5.1112 XPM226 B

AdTxr39t…YrmoMLar AQFBW6Ev…RQ4H4EFe

49fd2107f27c3b…7659128162f64f

1 in → 2 out6.6204 XPM225 B

AQXUSoBL…CzbjKp8b ANvtpRa1…QjsraDJz

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.

2.407 × 10⁹⁷(98-digit number)

24079909555145581027…13503478102709258240

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

2.407 × 10⁹⁷(98-digit number)

24079909555145581027…13503478102709258239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.407 × 10⁹⁷(98-digit number)

24079909555145581027…13503478102709258241

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

4.815 × 10⁹⁷(98-digit number)

48159819110291162055…27006956205418516479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.815 × 10⁹⁷(98-digit number)

48159819110291162055…27006956205418516481

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

9.631 × 10⁹⁷(98-digit number)

96319638220582324111…54013912410837032959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.631 × 10⁹⁷(98-digit number)

96319638220582324111…54013912410837032961

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

1.926 × 10⁹⁸(99-digit number)

19263927644116464822…08027824821674065919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.926 × 10⁹⁸(99-digit number)

19263927644116464822…08027824821674065921

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

3.852 × 10⁹⁸(99-digit number)

38527855288232929644…16055649643348131839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.852 × 10⁹⁸(99-digit number)

38527855288232929644…16055649643348131841

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 185545

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 83e53e0b2d76dcd11c5dceb21e2c4bf5657ea11b4ca9d452e188cba9e35f81d6

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 #185,545 on Chainz ↗