Home/Chain Registry/Block #218,826

Block #218,826

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 4:04:31 AM · Difficulty 9.9314 · 6,608,421 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a9ff9bd219ef829220c7b9cdb444a350c507a3b20737e32e8d73090e7e5e894

View on Chainz ↗

Height

#218,826

Difficulty

9.931352

Transactions

Size

764 B

Version

Bits

09ee6d10

Nonce

265,664

Timestamp

10/20/2013, 4:04:31 AM

Confirmations

6,608,421

Merkle Root

b3c2917b72890ea1da955d9c69c6da0494c9f2d091d6f7fcafd9070f2f59e714

Transactions (1)

Coinbaseb3c2917b72890e…d9070f2f59e714

1 in → 18 out10.1179 XPM674 B

AdnG9gQ7…N9B7mA2p AbeUZSvK…ijGzuyjz ARg8Kp4c…n7AUWZXy AXpmXsTH…1zkdde3r AKDTDDtx…iqvw9cdY

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.

3.453 × 10⁹⁵(96-digit number)

34539390435978725056…96219398190610918400

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

3.453 × 10⁹⁵(96-digit number)

34539390435978725056…96219398190610918399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.453 × 10⁹⁵(96-digit number)

34539390435978725056…96219398190610918401

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

6.907 × 10⁹⁵(96-digit number)

69078780871957450113…92438796381221836799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.907 × 10⁹⁵(96-digit number)

69078780871957450113…92438796381221836801

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

1.381 × 10⁹⁶(97-digit number)

13815756174391490022…84877592762443673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.381 × 10⁹⁶(97-digit number)

13815756174391490022…84877592762443673601

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

2.763 × 10⁹⁶(97-digit number)

27631512348782980045…69755185524887347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.763 × 10⁹⁶(97-digit number)

27631512348782980045…69755185524887347201

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

5.526 × 10⁹⁶(97-digit number)

55263024697565960090…39510371049774694399

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 218826

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 8a9ff9bd219ef829220c7b9cdb444a350c507a3b20737e32e8d73090e7e5e894

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 #218,826 on Chainz ↗

Block #218,826

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