Home/Chain Registry/Block #198,054

Block #198,054

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/7/2013, 12:32:20 PM · Difficulty 9.8842 · 6,600,945 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

256675de51a49f8686fa281131551390e3ad3ab33eebbf1448e67164b837dfd4

View on Chainz ↗

Height

#198,054

Difficulty

9.884159

Transactions

Size

1.14 KB

Version

Bits

09e25844

Nonce

419,374

Timestamp

10/7/2013, 12:32:20 PM

Confirmations

6,600,945

Merkle Root

bca35277101cc6d195fc983bc61585cf08a681a60299fa644e65c28d040572db

Transactions (2)

Coinbase1a74a57a648ea9…e383471fa36fc9

1 in → 1 out10.2300 XPM109 B

ANjoZavn…VrcsapZU

0af2e7bddb1198…2093fe35027b1d

6 in → 2 out29.1380 XPM964 B

AKwNsmdD…fLEajU4R AaLi7mGy…4HRSbNdq

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.

9.004 × 10⁹⁵(96-digit number)

90042255720184359446…04298162285631680960

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

9.004 × 10⁹⁵(96-digit number)

90042255720184359446…04298162285631680959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.004 × 10⁹⁵(96-digit number)

90042255720184359446…04298162285631680961

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

1.800 × 10⁹⁶(97-digit number)

18008451144036871889…08596324571263361919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.800 × 10⁹⁶(97-digit number)

18008451144036871889…08596324571263361921

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

3.601 × 10⁹⁶(97-digit number)

36016902288073743778…17192649142526723839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.601 × 10⁹⁶(97-digit number)

36016902288073743778…17192649142526723841

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

7.203 × 10⁹⁶(97-digit number)

72033804576147487557…34385298285053447679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.203 × 10⁹⁶(97-digit number)

72033804576147487557…34385298285053447681

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

1.440 × 10⁹⁷(98-digit number)

14406760915229497511…68770596570106895359

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 198054

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 256675de51a49f8686fa281131551390e3ad3ab33eebbf1448e67164b837dfd4

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 #198,054 on Chainz ↗