Home/Chain Registry/Block #294,908

Block #294,908

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 3:45:03 AM · Difficulty 9.9912 · 6,550,021 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

013b66e41dcbfb877535a107ee080ecb1e27dcf3a90679a486414ee85dd3d2c5

View on Chainz ↗

Height

#294,908

Difficulty

9.991176

Transactions

Size

4.15 KB

Version

Bits

09fdbdaf

Nonce

104,482

Timestamp

12/5/2013, 3:45:03 AM

Confirmations

6,550,021

Merkle Root

93720b6392a28b9ff51c759bc0d9da9c718bb7647fc833f9ba1ada26cf94bce7

Transactions (4)

Coinbase00416e8a750760…98ce49fcfa4484

1 in → 31 out9.9800 XPM1.09 KB

Ad9pSzHt…cpJ3y2zz ARcqMJhp…RVLToQ6S AHuJ9wYh…BGmgHrKZ AN63YyQR…1tfe566A Ac5sZcdP…kzV4eckG

6dffd3a91b1ddf…959ccdab59995a

14 in → 2 out18.4709 XPM2.10 KB

AUmFbGFh…p81PyP1h AdG4DBff…6AbtxBCw

1ebe7d8a8ff8bc…8d71178ce84116

3 in → 2 out10.5231 XPM520 B

AKc2zo7j…PxUhcLd3 AaPF4B6v…q12JbJxD

fe57a9919f5016…c6ed93a09e2afd

2 in → 2 out423.1300 XPM373 B

Ab6hvxZo…odBFQhHw AcGD1LHJ…ZHgx9g48

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.

4.226 × 10⁹²(93-digit number)

42261124496434558212…11279203982473520500

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

4.226 × 10⁹²(93-digit number)

42261124496434558212…11279203982473520499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.226 × 10⁹²(93-digit number)

42261124496434558212…11279203982473520501

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

8.452 × 10⁹²(93-digit number)

84522248992869116425…22558407964947040999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.452 × 10⁹²(93-digit number)

84522248992869116425…22558407964947041001

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

1.690 × 10⁹³(94-digit number)

16904449798573823285…45116815929894081999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.690 × 10⁹³(94-digit number)

16904449798573823285…45116815929894082001

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

3.380 × 10⁹³(94-digit number)

33808899597147646570…90233631859788163999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.380 × 10⁹³(94-digit number)

33808899597147646570…90233631859788164001

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

6.761 × 10⁹³(94-digit number)

67617799194295293140…80467263719576327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.761 × 10⁹³(94-digit number)

67617799194295293140…80467263719576328001

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 294908

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 013b66e41dcbfb877535a107ee080ecb1e27dcf3a90679a486414ee85dd3d2c5

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 #294,908 on Chainz ↗

Block #294,908

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