Home/Chain Registry/Block #850,041

Block #850,041

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2014, 5:59:17 AM · Difficulty 10.9713 · 5,994,881 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8c70e6eb0ca027a48b34e1f22c19c27964a2ea8f54d7614248428a14817949e2

View on Chainz ↗

Height

#850,041

Difficulty

10.971316

Transactions

Size

653 B

Version

Bits

0af8a82d

Nonce

151,360,720

Timestamp

12/12/2014, 5:59:17 AM

Confirmations

5,994,881

Merkle Root

c240ed75ead9f9052c18b1cdb30be0acf625d8dacbee934c918434bac90483f2

Transactions (3)

Coinbase8a1b87a0ecfebe…d5d44ca511691d

1 in → 1 out8.3200 XPM110 B

ALzHAGhn…G5dFUU5h

3c94646572212d…a7ebb6f60eec1c

1 in → 2 out0.0709 XPM226 B

AZv3beUo…yS18gmBA AUK5tUb5…PDyBUMdE

5cd372947c9c3c…65921b1fb0f331

1 in → 2 out0.0707 XPM226 B

AbBnqFAP…1iBiDCRy AYYTEZZr…MMrF611x

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.

3.568 × 10⁹⁶(97-digit number)

35687113787272319485…49037297088411555840

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

3.568 × 10⁹⁶(97-digit number)

35687113787272319485…49037297088411555839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.568 × 10⁹⁶(97-digit number)

35687113787272319485…49037297088411555841

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

7.137 × 10⁹⁶(97-digit number)

71374227574544638971…98074594176823111679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.137 × 10⁹⁶(97-digit number)

71374227574544638971…98074594176823111681

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

1.427 × 10⁹⁷(98-digit number)

14274845514908927794…96149188353646223359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.427 × 10⁹⁷(98-digit number)

14274845514908927794…96149188353646223361

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

2.854 × 10⁹⁷(98-digit number)

28549691029817855588…92298376707292446719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.854 × 10⁹⁷(98-digit number)

28549691029817855588…92298376707292446721

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

5.709 × 10⁹⁷(98-digit number)

57099382059635711177…84596753414584893439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.709 × 10⁹⁷(98-digit number)

57099382059635711177…84596753414584893441

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 850041

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 8c70e6eb0ca027a48b34e1f22c19c27964a2ea8f54d7614248428a14817949e2

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 #850,041 on Chainz ↗

Block #850,041

Cookie Preferences