Home/Chain Registry/Block #86,084

Block #86,084

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 9:35:08 PM · Difficulty 9.2887 · 6,703,780 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2284ca37a7cb027fb5c224d9a146c53fb172f72ee7c18d91b7d6e8e4a0e727f0

View on Chainz ↗

Height

#86,084

Difficulty

9.288750

Transactions

Size

206 B

Version

Bits

0949eb80

Nonce

133,013

Timestamp

7/27/2013, 9:35:08 PM

Confirmations

6,703,780

Merkle Root

2d0acdd25743399e1fd1dfe5d55ad1a1fdc81d65aafd8dea897be7c11c11e38f

Transactions (1)

Coinbase2d0acdd2574339…7be7c11c11e38f

1 in → 1 out11.5700 XPM109 B

AdPAiR9b…gEdrhwNh

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.

9.298 × 10¹¹⁰(111-digit number)

92983553351781016734…00519366387331025620

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

9.298 × 10¹¹⁰(111-digit number)

92983553351781016734…00519366387331025619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.298 × 10¹¹⁰(111-digit number)

92983553351781016734…00519366387331025621

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

1.859 × 10¹¹¹(112-digit number)

18596710670356203346…01038732774662051239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.859 × 10¹¹¹(112-digit number)

18596710670356203346…01038732774662051241

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

3.719 × 10¹¹¹(112-digit number)

37193421340712406693…02077465549324102479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.719 × 10¹¹¹(112-digit number)

37193421340712406693…02077465549324102481

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

7.438 × 10¹¹¹(112-digit number)

74386842681424813387…04154931098648204959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.438 × 10¹¹¹(112-digit number)

74386842681424813387…04154931098648204961

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

1.487 × 10¹¹²(113-digit number)

14877368536284962677…08309862197296409919

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 86084

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 2284ca37a7cb027fb5c224d9a146c53fb172f72ee7c18d91b7d6e8e4a0e727f0

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 #86,084 on Chainz ↗