Home/Chain Registry/Block #357,189

Block #357,189

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 6:11:44 AM · Difficulty 10.3825 · 6,457,617 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

353b3dd744b31ed41fbc090d113b59f461e871bd9df7136bb6f0b2d8a9306ea6

View on Chainz ↗

Height

#357,189

Difficulty

10.382491

Transactions

Size

659 B

Version

Bits

0a61eaed

Nonce

7,241

Timestamp

1/13/2014, 6:11:44 AM

Confirmations

6,457,617

Merkle Root

89c524bb617626b5523f2d65471dff093db3933a7bdd8b3ad3d6f71e5287055a

Transactions (3)

Coinbase912891f9514b2e…e544e841963640

1 in → 1 out9.2800 XPM116 B

AbwWkWZt…kawDhufa

07b58ea5913420…4077bca278f636

1 in → 2 out3.6126 XPM226 B

AZhnxGNS…yAbnbtUz AX7NAEpw…7t34YqHr

6bc4cfbae8eb57…727cf136d4c375

1 in → 2 out3.2111 XPM227 B

AGUiHrXX…99nzH74G AL4Ar4pu…FbZyBb5s

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.

3.284 × 10⁹³(94-digit number)

32845422433697532762…61735251519924152920

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

3.284 × 10⁹³(94-digit number)

32845422433697532762…61735251519924152919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.284 × 10⁹³(94-digit number)

32845422433697532762…61735251519924152921

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

6.569 × 10⁹³(94-digit number)

65690844867395065524…23470503039848305839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.569 × 10⁹³(94-digit number)

65690844867395065524…23470503039848305841

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

1.313 × 10⁹⁴(95-digit number)

13138168973479013104…46941006079696611679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.313 × 10⁹⁴(95-digit number)

13138168973479013104…46941006079696611681

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

2.627 × 10⁹⁴(95-digit number)

26276337946958026209…93882012159393223359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.627 × 10⁹⁴(95-digit number)

26276337946958026209…93882012159393223361

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

5.255 × 10⁹⁴(95-digit number)

52552675893916052419…87764024318786446719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.255 × 10⁹⁴(95-digit number)

52552675893916052419…87764024318786446721

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 357189

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 353b3dd744b31ed41fbc090d113b59f461e871bd9df7136bb6f0b2d8a9306ea6

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 #357,189 on Chainz ↗

Block #357,189

Cookie Preferences