Home/Chain Registry/Block #173,450

Block #173,450

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/20/2013, 11:57:32 PM · Difficulty 9.8607 · 6,653,632 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

18b1bdee47532f79f8eae0ed9868badd5febbe2d84b876de899d77586132face

View on Chainz ↗

Height

#173,450

Difficulty

9.860728

Transactions

Size

424 B

Version

Bits

09dc58aa

Nonce

37,027

Timestamp

9/20/2013, 11:57:32 PM

Confirmations

6,653,632

Merkle Root

7318eedf953b43798a5d6c8ef1c730d49f5d792a67df045ad3fe26c75608a7e0

Transactions (2)

Coinbase64cf10999af825…a134c75f569076

1 in → 1 out10.2800 XPM109 B

AYKFccHZ…CdXZ542n

0b178af4968344…c8f5e21fbee6b7

1 in → 2 out3.9371 XPM225 B

AVYebXcy…Hb6vMiyi AY87mhKr…gFVkhB4D

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.

1.016 × 10⁹⁴(95-digit number)

10165499336494232236…01213724356003734560

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

1.016 × 10⁹⁴(95-digit number)

10165499336494232236…01213724356003734559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.016 × 10⁹⁴(95-digit number)

10165499336494232236…01213724356003734561

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

2.033 × 10⁹⁴(95-digit number)

20330998672988464472…02427448712007469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.033 × 10⁹⁴(95-digit number)

20330998672988464472…02427448712007469121

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

4.066 × 10⁹⁴(95-digit number)

40661997345976928944…04854897424014938239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.066 × 10⁹⁴(95-digit number)

40661997345976928944…04854897424014938241

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

8.132 × 10⁹⁴(95-digit number)

81323994691953857888…09709794848029876479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.132 × 10⁹⁴(95-digit number)

81323994691953857888…09709794848029876481

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

1.626 × 10⁹⁵(96-digit number)

16264798938390771577…19419589696059752959

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.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

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 173450

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 18b1bdee47532f79f8eae0ed9868badd5febbe2d84b876de899d77586132face

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 #173,450 on Chainz ↗

Block #173,450

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