Home/Chain Registry/Block #83,406

Block #83,406

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 3:24:24 AM · Difficulty 9.2675 · 6,708,423 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

28925ea847cc8285a3686ff718fee62156e06e27d7f062c2f9756da2d2b90ec4

View on Chainz ↗

Height

#83,406

Difficulty

9.267457

Transactions

Size

204 B

Version

Bits

0944780f

Nonce

70,943

Timestamp

7/26/2013, 3:24:24 AM

Confirmations

6,708,423

Merkle Root

73f201fed7cbaffbabd7f6561fb8ff5fa1a5c7a02bca62a1eee0162e24a69500

Transactions (1)

Coinbase73f201fed7cbaf…e0162e24a69500

1 in → 1 out11.6300 XPM109 B

AcuJraLT…Y66BS47Q

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.

3.174 × 10¹⁰⁷(108-digit number)

31746558799330762510…19727079891934367700

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

3.174 × 10¹⁰⁷(108-digit number)

31746558799330762510…19727079891934367699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.174 × 10¹⁰⁷(108-digit number)

31746558799330762510…19727079891934367701

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

6.349 × 10¹⁰⁷(108-digit number)

63493117598661525021…39454159783868735399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.349 × 10¹⁰⁷(108-digit number)

63493117598661525021…39454159783868735401

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

1.269 × 10¹⁰⁸(109-digit number)

12698623519732305004…78908319567737470799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.269 × 10¹⁰⁸(109-digit number)

12698623519732305004…78908319567737470801

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

2.539 × 10¹⁰⁸(109-digit number)

25397247039464610008…57816639135474941599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.539 × 10¹⁰⁸(109-digit number)

25397247039464610008…57816639135474941601

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

5.079 × 10¹⁰⁸(109-digit number)

50794494078929220017…15633278270949883199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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 83406

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 28925ea847cc8285a3686ff718fee62156e06e27d7f062c2f9756da2d2b90ec4

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 #83,406 on Chainz ↗