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Block #38,799

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 12:31:32 PM · Difficulty 8.2358 · 6,770,354 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

320a6c6262b9e0081e308ddf3e5d2ff7aeaf01d5444ee8ea1a979c2fc44e4ab5

View on Chainz ↗

Height

#38,799

Difficulty

8.235768

Transactions

Size

208 B

Version

Bits

083c5b43

Nonce

668

Timestamp

7/14/2013, 12:31:32 PM

Confirmations

6,770,354

Merkle Root

d2f0bf84bb886e3868fe1db1251c85b86ee146ee385ba0e928ac3fa6361950bb

Transactions (1)

Coinbased2f0bf84bb886e…ac3fa6361950bb

1 in → 1 out14.7200 XPM110 B

AKsLKPc8…zkBgUqcr

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.

2.875 × 10¹¹⁴(115-digit number)

28751912068659773620…03506332521470126800

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

2.875 × 10¹¹⁴(115-digit number)

28751912068659773620…03506332521470126799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.875 × 10¹¹⁴(115-digit number)

28751912068659773620…03506332521470126801

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

5.750 × 10¹¹⁴(115-digit number)

57503824137319547241…07012665042940253599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.750 × 10¹¹⁴(115-digit number)

57503824137319547241…07012665042940253601

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

1.150 × 10¹¹⁵(116-digit number)

11500764827463909448…14025330085880507199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.150 × 10¹¹⁵(116-digit number)

11500764827463909448…14025330085880507201

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

2.300 × 10¹¹⁵(116-digit number)

23001529654927818896…28050660171761014399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.300 × 10¹¹⁵(116-digit number)

23001529654927818896…28050660171761014401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 38799

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 320a6c6262b9e0081e308ddf3e5d2ff7aeaf01d5444ee8ea1a979c2fc44e4ab5

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 #38,799 on Chainz ↗

Block #38,799

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