Home/Chain Registry/Block #186,184

Block #186,184

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 6:34:25 PM · Difficulty 9.8646 · 6,605,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9d863086d3d6f9a1343972b1f39666aaf1f7a6712d0fae90094e19be2ce4c14

View on Chainz ↗

Height

#186,184

Difficulty

9.864551

Transactions

Size

200 B

Version

Bits

09dd533c

Nonce

15,437

Timestamp

9/29/2013, 6:34:25 PM

Confirmations

6,605,173

Merkle Root

53d5cb7ab8b5b1ec320bc0e1f0114da8b31c926fd2f1e25acb73698498b4646f

Transactions (1)

Coinbase53d5cb7ab8b5b1…73698498b4646f

1 in → 1 out10.2600 XPM109 B

Aa3nXMze…pSXZcaRL

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.

2.457 × 10⁹⁶(97-digit number)

24578513063138863851…76163870995830347840

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

2.457 × 10⁹⁶(97-digit number)

24578513063138863851…76163870995830347839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.457 × 10⁹⁶(97-digit number)

24578513063138863851…76163870995830347841

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

4.915 × 10⁹⁶(97-digit number)

49157026126277727702…52327741991660695679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.915 × 10⁹⁶(97-digit number)

49157026126277727702…52327741991660695681

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

9.831 × 10⁹⁶(97-digit number)

98314052252555455405…04655483983321391359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.831 × 10⁹⁶(97-digit number)

98314052252555455405…04655483983321391361

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

1.966 × 10⁹⁷(98-digit number)

19662810450511091081…09310967966642782719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.966 × 10⁹⁷(98-digit number)

19662810450511091081…09310967966642782721

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

3.932 × 10⁹⁷(98-digit number)

39325620901022182162…18621935933285565439

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 186184

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 e9d863086d3d6f9a1343972b1f39666aaf1f7a6712d0fae90094e19be2ce4c14

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 #186,184 on Chainz ↗