Home/Chain Registry/Block #105,234

Block #105,234

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/8/2013, 10:32:12 AM · Difficulty 9.5784 · 6,687,826 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa2295e84af1fac4bee8e31cd03aaf681e083b410f33f8a8a837704369105516

View on Chainz ↗

Height

#105,234

Difficulty

9.578443

Transactions

Size

2.27 KB

Version

Bits

099414d1

Nonce

661,473

Timestamp

8/8/2013, 10:32:12 AM

Confirmations

6,687,826

Merkle Root

43ee2c20488ec12cc65f8e35422820ee80655c8ab3d2cb6f337bdfb1166d869e

Transactions (2)

Coinbase38212bbdb33d33…9e55f1996e0bcc

1 in → 1 out10.9100 XPM109 B

AX99MLNm…vtidqEwE

4b3064f78ab69c…429998dcab2bb5

18 in → 2 out200.3600 XPM2.08 KB

AdNeXXkk…QpfXAns4 AbbfEB62…4hPdVXHo

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.

5.705 × 10⁹⁴(95-digit number)

57053888049285368987…33932915432789685040

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

5.705 × 10⁹⁴(95-digit number)

57053888049285368987…33932915432789685039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.705 × 10⁹⁴(95-digit number)

57053888049285368987…33932915432789685041

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

1.141 × 10⁹⁵(96-digit number)

11410777609857073797…67865830865579370079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.141 × 10⁹⁵(96-digit number)

11410777609857073797…67865830865579370081

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

2.282 × 10⁹⁵(96-digit number)

22821555219714147595…35731661731158740159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.282 × 10⁹⁵(96-digit number)

22821555219714147595…35731661731158740161

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

4.564 × 10⁹⁵(96-digit number)

45643110439428295190…71463323462317480319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.564 × 10⁹⁵(96-digit number)

45643110439428295190…71463323462317480321

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

9.128 × 10⁹⁵(96-digit number)

91286220878856590380…42926646924634960639

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 105234

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 aa2295e84af1fac4bee8e31cd03aaf681e083b410f33f8a8a837704369105516

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 #105,234 on Chainz ↗