Home/Chain Registry/Block #161,524

Block #161,524

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/12/2013, 5:34:17 PM · Difficulty 9.8595 · 6,656,308 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

04b431f3bdcbcedf7e69266b33bb2e3d718dbfe6078fbb2a8e6b0fda41e67f97

View on Chainz ↗

Height

#161,524

Difficulty

9.859468

Transactions

Size

389 B

Version

Bits

09dc0615

Nonce

256,728

Timestamp

9/12/2013, 5:34:17 PM

Confirmations

6,656,308

Merkle Root

34ef4194f1de2579390a07c59fcc4a3eb1db9cf91d418d93ce39975531073527

Transactions (2)

Coinbasea9a8b05d55be61…2a2d3326e4ed2d

1 in → 1 out10.2800 XPM109 B

AZ6tNwWZ…sY8faWM4

8a81875eb81457…6b9f7935b20993

1 in → 2 out10.2400 XPM192 B

AW1p4LF5…CxQPXYQi AaiQ25kC…uarGkYVE

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.

6.597 × 10⁹⁰(91-digit number)

65971940819575329203…57850338054171254420

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

6.597 × 10⁹⁰(91-digit number)

65971940819575329203…57850338054171254419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.597 × 10⁹⁰(91-digit number)

65971940819575329203…57850338054171254421

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

1.319 × 10⁹¹(92-digit number)

13194388163915065840…15700676108342508839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.319 × 10⁹¹(92-digit number)

13194388163915065840…15700676108342508841

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

2.638 × 10⁹¹(92-digit number)

26388776327830131681…31401352216685017679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.638 × 10⁹¹(92-digit number)

26388776327830131681…31401352216685017681

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

5.277 × 10⁹¹(92-digit number)

52777552655660263363…62802704433370035359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.277 × 10⁹¹(92-digit number)

52777552655660263363…62802704433370035361

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

1.055 × 10⁹²(93-digit number)

10555510531132052672…25605408866740070719

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 161524

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 04b431f3bdcbcedf7e69266b33bb2e3d718dbfe6078fbb2a8e6b0fda41e67f97

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 #161,524 on Chainz ↗

Block #161,524

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