Home/Chain Registry/Block #356,098

Block #356,098

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 1:26:02 PM · Difficulty 10.3717 · 6,444,707 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6180bdfad4583dfe1d1845b5ba9bd8117a7f11fb6c8ee8f8b05896bcc2f93db

View on Chainz ↗

Height

#356,098

Difficulty

10.371661

Transactions

Size

217 B

Version

Bits

0a5f252b

Nonce

5,570

Timestamp

1/12/2014, 1:26:02 PM

Confirmations

6,444,707

Merkle Root

f82b4d07b2c2b0e6e28eb7142b569c78f90c2cfd8a1934150eecc83a9df6458c

Transactions (1)

Coinbasef82b4d07b2c2b0…ecc83a9df6458c

1 in → 1 out9.2800 XPM116 B

AbwWkWZt…kawDhufa

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.

1.008 × 10¹²¹(122-digit number)

10081555882912344489…94721203978607001600

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

1.008 × 10¹²¹(122-digit number)

10081555882912344489…94721203978607001599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.008 × 10¹²¹(122-digit number)

10081555882912344489…94721203978607001601

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

2.016 × 10¹²¹(122-digit number)

20163111765824688978…89442407957214003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.016 × 10¹²¹(122-digit number)

20163111765824688978…89442407957214003201

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

4.032 × 10¹²¹(122-digit number)

40326223531649377956…78884815914428006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.032 × 10¹²¹(122-digit number)

40326223531649377956…78884815914428006401

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

8.065 × 10¹²¹(122-digit number)

80652447063298755912…57769631828856012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.065 × 10¹²¹(122-digit number)

80652447063298755912…57769631828856012801

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

1.613 × 10¹²²(123-digit number)

16130489412659751182…15539263657712025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.613 × 10¹²²(123-digit number)

16130489412659751182…15539263657712025601

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 356098

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 a6180bdfad4583dfe1d1845b5ba9bd8117a7f11fb6c8ee8f8b05896bcc2f93db

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 #356,098 on Chainz ↗