Home/Chain Registry/Block #29,247

Block #29,247

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 2:52:57 PM · Difficulty 7.9841 · 6,772,230 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

819c809c183d324eaafbd94326e40d247d1c0e80567450aed0bce7804549f4e4

View on Chainz ↗

Height

#29,247

Difficulty

7.984145

Transactions

Size

578 B

Version

Bits

07fbf0ef

Nonce

945

Timestamp

7/13/2013, 2:52:57 PM

Confirmations

6,772,230

Merkle Root

0740a84a32d7685dcb37a890aaeec6c6072712554770f4e81d1716330d1cc68d

Transactions (2)

Coinbase063ff94c036b1d…ab375952a6bc3d

1 in → 1 out15.6800 XPM108 B

AZcVptqU…h4YGesA9

c313a9e112804d…a5202b13091ab1

2 in → 2 out67.9800 XPM374 B

AcHw6bHF…rQyhBw66 AHwxuGf7…Yg4mX1e8

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.

6.811 × 10¹⁰⁸(109-digit number)

68119400582006798971…91895196232655835030

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

6.811 × 10¹⁰⁸(109-digit number)

68119400582006798971…91895196232655835029

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.811 × 10¹⁰⁸(109-digit number)

68119400582006798971…91895196232655835031

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

1.362 × 10¹⁰⁹(110-digit number)

13623880116401359794…83790392465311670059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.362 × 10¹⁰⁹(110-digit number)

13623880116401359794…83790392465311670061

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

2.724 × 10¹⁰⁹(110-digit number)

27247760232802719588…67580784930623340119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.724 × 10¹⁰⁹(110-digit number)

27247760232802719588…67580784930623340121

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

5.449 × 10¹⁰⁹(110-digit number)

54495520465605439176…35161569861246680239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 29247

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 819c809c183d324eaafbd94326e40d247d1c0e80567450aed0bce7804549f4e4

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 #29,247 on Chainz ↗