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Block #846,015

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/9/2014, 7:29:18 AM · Difficulty 10.9723 · 5,996,975 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dd3838d07550a9d60382997e6d83cb17abf4a00b02e0a2cf779361ed8a2c3cb0

View on Chainz ↗

Height

#846,015

Difficulty

10.972325

Transactions

Size

654 B

Version

Bits

0af8ea4d

Nonce

395,007,333

Timestamp

12/9/2014, 7:29:18 AM

Confirmations

5,996,975

Merkle Root

5049b0c5d57fc1e468f40fe55b2a8c0dc921b972a935a579a2d7efc178e09e87

Transactions (3)

Coinbase34f818768c1523…3404d716af20dc

1 in → 1 out8.3200 XPM110 B

AVcccXjp…JNEeD4s2

9b518a4159bbfb…f255047a9f0dee

1 in → 2 out0.4257 XPM226 B

AYiE45UD…CuczXbBv ATq7auzu…UNV9THk2

d2b70e80b3a42c…cd42c1197e91ae

1 in → 2 out0.0373 XPM227 B

AZY9ULVm…Wz46qhcQ AaXCCBCz…tzCywBVC

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.

1.338 × 10⁹⁶(97-digit number)

13389593845247240067…17614747539453926400

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

1.338 × 10⁹⁶(97-digit number)

13389593845247240067…17614747539453926399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.338 × 10⁹⁶(97-digit number)

13389593845247240067…17614747539453926401

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

2.677 × 10⁹⁶(97-digit number)

26779187690494480135…35229495078907852799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.677 × 10⁹⁶(97-digit number)

26779187690494480135…35229495078907852801

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

5.355 × 10⁹⁶(97-digit number)

53558375380988960270…70458990157815705599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.355 × 10⁹⁶(97-digit number)

53558375380988960270…70458990157815705601

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

1.071 × 10⁹⁷(98-digit number)

10711675076197792054…40917980315631411199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.071 × 10⁹⁷(98-digit number)

10711675076197792054…40917980315631411201

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

2.142 × 10⁹⁷(98-digit number)

21423350152395584108…81835960631262822399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.142 × 10⁹⁷(98-digit number)

21423350152395584108…81835960631262822401

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 846015

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 dd3838d07550a9d60382997e6d83cb17abf4a00b02e0a2cf779361ed8a2c3cb0

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 #846,015 on Chainz ↗

Block #846,015

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