Home/Chain Registry/Block #106,893

Block #106,893

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/9/2013, 6:00:16 AM · Difficulty 9.6177 · 6,693,467 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee2494401bbc600c9b00dfbf9993f5e0300953cb320e2274ec796315502be302

View on Chainz ↗

Height

#106,893

Difficulty

9.617723

Transactions

Size

210 B

Version

Bits

099e231e

Nonce

474,432

Timestamp

8/9/2013, 6:00:16 AM

Confirmations

6,693,467

Merkle Root

c017c97ddcfacc6b7bbcb199284cd688c730237ebdad98e3c8757e66ffd34371

Transactions (1)

Coinbasec017c97ddcfacc…757e66ffd34371

1 in → 1 out10.7900 XPM112 B

AT5A2KL6…CT16n6i2

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.

9.272 × 10¹¹⁴(115-digit number)

92724035491897632063…35926052760013623520

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

9.272 × 10¹¹⁴(115-digit number)

92724035491897632063…35926052760013623519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.272 × 10¹¹⁴(115-digit number)

92724035491897632063…35926052760013623521

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

1.854 × 10¹¹⁵(116-digit number)

18544807098379526412…71852105520027247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.854 × 10¹¹⁵(116-digit number)

18544807098379526412…71852105520027247041

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

3.708 × 10¹¹⁵(116-digit number)

37089614196759052825…43704211040054494079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.708 × 10¹¹⁵(116-digit number)

37089614196759052825…43704211040054494081

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

7.417 × 10¹¹⁵(116-digit number)

74179228393518105650…87408422080108988159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.417 × 10¹¹⁵(116-digit number)

74179228393518105650…87408422080108988161

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

1.483 × 10¹¹⁶(117-digit number)

14835845678703621130…74816844160217976319

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 106893

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 ee2494401bbc600c9b00dfbf9993f5e0300953cb320e2274ec796315502be302

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 #106,893 on Chainz ↗