Home/Chain Registry/Block #138,090

Block #138,090

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/28/2013, 5:07:55 AM · Difficulty 9.8243 · 6,662,555 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05ff4a6d4fd353f0d4eb0d3201a898afdb1599525db2d7894d07428c7a917af6

View on Chainz ↗

Height

#138,090

Difficulty

9.824348

Transactions

Size

877 B

Version

Bits

09d3087b

Nonce

62,259

Timestamp

8/28/2013, 5:07:55 AM

Confirmations

6,662,555

Merkle Root

524ebf5fe5845f36e279177701244f558ae2542a6f90b812d53534455eded6d2

Transactions (2)

Coinbase517117400cbdc9…8abdca0bd19917

1 in → 1 out10.3600 XPM109 B

AHi3xmoJ…NUhUJ9tj

011e9db63037c5…b5214233a35c37

5 in → 2 out42.1100 XPM680 B

AFv2HUwU…rHhs8Nj9 AK2gycCd…dEXQ9SUu

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.

3.490 × 10⁹⁰(91-digit number)

34908731119876095571…03319824194411886600

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

3.490 × 10⁹⁰(91-digit number)

34908731119876095571…03319824194411886599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.490 × 10⁹⁰(91-digit number)

34908731119876095571…03319824194411886601

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

6.981 × 10⁹⁰(91-digit number)

69817462239752191142…06639648388823773199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.981 × 10⁹⁰(91-digit number)

69817462239752191142…06639648388823773201

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

1.396 × 10⁹¹(92-digit number)

13963492447950438228…13279296777647546399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.396 × 10⁹¹(92-digit number)

13963492447950438228…13279296777647546401

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

2.792 × 10⁹¹(92-digit number)

27926984895900876456…26558593555295092799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.792 × 10⁹¹(92-digit number)

27926984895900876456…26558593555295092801

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

5.585 × 10⁹¹(92-digit number)

55853969791801752913…53117187110590185599

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 138090

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 05ff4a6d4fd353f0d4eb0d3201a898afdb1599525db2d7894d07428c7a917af6

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 #138,090 on Chainz ↗