Home/Chain Registry/Block #306,759

Block #306,759

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 5:41:09 AM · Difficulty 9.9940 · 6,485,837 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1aab9fa0d5dc98114f3f2dbf93da688be3f9f08efb36771f0ac9c6009e7d701c

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Height

#306,759

Difficulty

9.993972

Transactions

Size

1.05 KB

Version

Bits

09fe74f4

Nonce

137,563

Timestamp

12/12/2013, 5:41:09 AM

Confirmations

6,485,837

Merkle Root

d4904799aa24a2f185c059c2b2454bcf200db377a05ff59a20fd883f0de83bcd

Transactions (1)

Coinbased4904799aa24a2…fd883f0de83bcd

1 in → 27 out10.0000 XPM981 B

AdwTEXyC…NwbVbqZV Ad9pSzHt…cpJ3y2zz AZrL7RMy…wiqRKgBv AMPcXbqv…fK7wHymz AQRsMcRR…TwMr7sTF

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.

3.536 × 10⁹⁴(95-digit number)

35365656028991031295…47602354364591752000

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

3.536 × 10⁹⁴(95-digit number)

35365656028991031295…47602354364591751999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.536 × 10⁹⁴(95-digit number)

35365656028991031295…47602354364591752001

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

7.073 × 10⁹⁴(95-digit number)

70731312057982062590…95204708729183503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.073 × 10⁹⁴(95-digit number)

70731312057982062590…95204708729183504001

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

1.414 × 10⁹⁵(96-digit number)

14146262411596412518…90409417458367007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.414 × 10⁹⁵(96-digit number)

14146262411596412518…90409417458367008001

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

2.829 × 10⁹⁵(96-digit number)

28292524823192825036…80818834916734015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.829 × 10⁹⁵(96-digit number)

28292524823192825036…80818834916734016001

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

5.658 × 10⁹⁵(96-digit number)

56585049646385650072…61637669833468031999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.658 × 10⁹⁵(96-digit number)

56585049646385650072…61637669833468032001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 306759

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 1aab9fa0d5dc98114f3f2dbf93da688be3f9f08efb36771f0ac9c6009e7d701c

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 #306,759 on Chainz ↗