Home/Chain Registry/Block #86,358

Block #86,358

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 1:58:47 AM · Difficulty 9.2904 · 6,706,720 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

289f8a05d0cee040740bcc531c3a04227090045ceaaf023a355e925aa5912e2e

View on Chainz ↗

Height

#86,358

Difficulty

9.290371

Transactions

Size

354 B

Version

Bits

094a55c9

Nonce

58,874

Timestamp

7/28/2013, 1:58:47 AM

Confirmations

6,706,720

Merkle Root

01858baf28df8ad99e9c1ee3b5bfbcba9fc4a7fd0b7b168440b9f7ebea5da2bb

Transactions (2)

Coinbase03d97a4ff0e6df…1d89c140c398dd

1 in → 1 out11.5800 XPM109 B

AcuJraLT…Y66BS47Q

6a9930c3aca1ce…5c3db2b43dea59

1 in → 1 out11.6600 XPM157 B

AHHWdDed…68fA6bQR

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.

2.075 × 10⁹⁰(91-digit number)

20757664978785916485…03776976752339927280

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

2.075 × 10⁹⁰(91-digit number)

20757664978785916485…03776976752339927279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.075 × 10⁹⁰(91-digit number)

20757664978785916485…03776976752339927281

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

4.151 × 10⁹⁰(91-digit number)

41515329957571832971…07553953504679854559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.151 × 10⁹⁰(91-digit number)

41515329957571832971…07553953504679854561

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

8.303 × 10⁹⁰(91-digit number)

83030659915143665943…15107907009359709119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.303 × 10⁹⁰(91-digit number)

83030659915143665943…15107907009359709121

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

1.660 × 10⁹¹(92-digit number)

16606131983028733188…30215814018719418239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.660 × 10⁹¹(92-digit number)

16606131983028733188…30215814018719418241

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

3.321 × 10⁹¹(92-digit number)

33212263966057466377…60431628037438836479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.321 × 10⁹¹(92-digit number)

33212263966057466377…60431628037438836481

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 86358

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 289f8a05d0cee040740bcc531c3a04227090045ceaaf023a355e925aa5912e2e

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 #86,358 on Chainz ↗