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Block #234,079

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 2:50:59 AM · Difficulty 9.9435 · 6,610,964 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b289aa09c6da1b9419d36a4b69d391f15cdc64b5255375e7204df356ad3c4151

View on Chainz ↗

Height

#234,079

Difficulty

9.943469

Transactions

Size

2.08 KB

Version

Bits

09f18734

Nonce

134,889

Timestamp

10/30/2013, 2:50:59 AM

Confirmations

6,610,964

Merkle Root

2bf90eebcfa057fc6316812a80abab5417ad2ed8b4c429e80a5151c86054abdc

Transactions (3)

Coinbasec9c7524650417d…6ec3148e6601d4

1 in → 1 out10.1300 XPM109 B

ARJ9U91q…5bSgmQwr

30fb39812cd279…001a544636b7de

5 in → 2 out2.7912 XPM820 B

Aa6pumzd…6LtHJKQX ALnigaPF…X4BFpZhn

577c9a73404088…020e823ab151a9

7 in → 2 out185.5183 XPM1.09 KB

AVJQRNHs…m8zAMztN AeZRDEiC…qZULtw7y

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.

2.507 × 10⁹⁵(96-digit number)

25072505234409780787…65180393362467501400

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

2.507 × 10⁹⁵(96-digit number)

25072505234409780787…65180393362467501399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.507 × 10⁹⁵(96-digit number)

25072505234409780787…65180393362467501401

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

5.014 × 10⁹⁵(96-digit number)

50145010468819561575…30360786724935002799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.014 × 10⁹⁵(96-digit number)

50145010468819561575…30360786724935002801

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

1.002 × 10⁹⁶(97-digit number)

10029002093763912315…60721573449870005599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.002 × 10⁹⁶(97-digit number)

10029002093763912315…60721573449870005601

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

2.005 × 10⁹⁶(97-digit number)

20058004187527824630…21443146899740011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.005 × 10⁹⁶(97-digit number)

20058004187527824630…21443146899740011201

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

4.011 × 10⁹⁶(97-digit number)

40116008375055649260…42886293799480022399

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 234079

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 b289aa09c6da1b9419d36a4b69d391f15cdc64b5255375e7204df356ad3c4151

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 #234,079 on Chainz ↗

Block #234,079

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