Home/Chain Registry/Block #79,805

Block #79,805

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/23/2013, 6:06:35 PM · Difficulty 9.2431 · 6,710,071 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c934c6004b8af1fbf241225194d6c03f85e0a1e3ed0d26dd64ab70154237387d

View on Chainz ↗

Height

#79,805

Difficulty

9.243132

Transactions

Size

201 B

Version

Bits

093e3de5

Nonce

184

Timestamp

7/23/2013, 6:06:35 PM

Confirmations

6,710,071

Merkle Root

4c03ff81557c7a06d48f798a220d2345e3fb0323a3277249c76bb8bb5e40fc07

Transactions (1)

Coinbase4c03ff81557c7a…6bb8bb5e40fc07

1 in → 1 out11.6900 XPM110 B

AVe9FWu7…86bzSbiC

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.

4.978 × 10⁹⁷(98-digit number)

49789040428071752052…85944588148874658500

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

4.978 × 10⁹⁷(98-digit number)

49789040428071752052…85944588148874658499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.978 × 10⁹⁷(98-digit number)

49789040428071752052…85944588148874658501

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

9.957 × 10⁹⁷(98-digit number)

99578080856143504104…71889176297749316999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.957 × 10⁹⁷(98-digit number)

99578080856143504104…71889176297749317001

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

1.991 × 10⁹⁸(99-digit number)

19915616171228700820…43778352595498633999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.991 × 10⁹⁸(99-digit number)

19915616171228700820…43778352595498634001

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

3.983 × 10⁹⁸(99-digit number)

39831232342457401641…87556705190997267999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.983 × 10⁹⁸(99-digit number)

39831232342457401641…87556705190997268001

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

7.966 × 10⁹⁸(99-digit number)

79662464684914803283…75113410381994535999

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 79805

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 c934c6004b8af1fbf241225194d6c03f85e0a1e3ed0d26dd64ab70154237387d

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 #79,805 on Chainz ↗