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Block #845,150

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/8/2014, 4:08:27 PM · Difficulty 10.9726 · 5,997,796 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4037abd606977f50726470c29c3fb7e6d575d70318b145fb843a6ac2de15e4c7

View on Chainz ↗

Height

#845,150

Difficulty

10.972601

Transactions

Size

433 B

Version

Bits

0af8fc59

Nonce

708,238,081

Timestamp

12/8/2014, 4:08:27 PM

Confirmations

5,997,796

Merkle Root

1794bd9b5874d4119246b2c56bde373e98732cc7f58af9410930008339b16846

Transactions (2)

Coinbase0603945d184efa…88ace3ced30295

1 in → 1 out8.3000 XPM116 B

ANSXnLY2…Sd25TjkD

b3f8e1fb2803e5…cfac25847d8535

1 in → 2 out507.7900 XPM226 B

AKVzbDAN…J8RE2osj AMN6qDkt…VuvvTq6f

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.

1.163 × 10⁹⁶(97-digit number)

11632821728387886532…39587891272548461120

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

1.163 × 10⁹⁶(97-digit number)

11632821728387886532…39587891272548461119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.163 × 10⁹⁶(97-digit number)

11632821728387886532…39587891272548461121

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

2.326 × 10⁹⁶(97-digit number)

23265643456775773065…79175782545096922239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.326 × 10⁹⁶(97-digit number)

23265643456775773065…79175782545096922241

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

4.653 × 10⁹⁶(97-digit number)

46531286913551546130…58351565090193844479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.653 × 10⁹⁶(97-digit number)

46531286913551546130…58351565090193844481

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

9.306 × 10⁹⁶(97-digit number)

93062573827103092261…16703130180387688959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.306 × 10⁹⁶(97-digit number)

93062573827103092261…16703130180387688961

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

1.861 × 10⁹⁷(98-digit number)

18612514765420618452…33406260360775377919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.861 × 10⁹⁷(98-digit number)

18612514765420618452…33406260360775377921

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.722 × 10⁹⁷(98-digit number)

37225029530841236904…66812520721550755839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 845150

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 4037abd606977f50726470c29c3fb7e6d575d70318b145fb843a6ac2de15e4c7

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 #845,150 on Chainz ↗

Block #845,150

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