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Block #86,786

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 9:32:59 AM · Difficulty 9.2866 · 6,712,459 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ff8e80aa3c48187be577276187808db187682293a26d69325d073f1711769ea

View on Chainz ↗

Height

#86,786

Difficulty

9.286584

Transactions

Size

873 B

Version

Bits

09495d98

Nonce

35,884

Timestamp

7/28/2013, 9:32:59 AM

Confirmations

6,712,459

Merkle Root

5f73822db9414acac402f9bb9a52585b387d973c426c0f5c6f80b7650ef3e3db

Transactions (2)

Coinbaseca2355750fb4f2…730f85ef647d3d

1 in → 1 out11.5900 XPM109 B

AcBadmkp…GmhL921o

454803fc7811ba…e0dbff0d150661

4 in → 2 out3.1732 XPM668 B

AaNMrVuB…vz8xMmHF Ad6HBhbo…Uw7zbr6P

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.

1.158 × 10¹⁰⁹(110-digit number)

11588072065835312335…44164613851851070080

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

1.158 × 10¹⁰⁹(110-digit number)

11588072065835312335…44164613851851070079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.158 × 10¹⁰⁹(110-digit number)

11588072065835312335…44164613851851070081

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

2.317 × 10¹⁰⁹(110-digit number)

23176144131670624671…88329227703702140159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.317 × 10¹⁰⁹(110-digit number)

23176144131670624671…88329227703702140161

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

4.635 × 10¹⁰⁹(110-digit number)

46352288263341249342…76658455407404280319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.635 × 10¹⁰⁹(110-digit number)

46352288263341249342…76658455407404280321

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

9.270 × 10¹⁰⁹(110-digit number)

92704576526682498684…53316910814808560639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.270 × 10¹⁰⁹(110-digit number)

92704576526682498684…53316910814808560641

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

1.854 × 10¹¹⁰(111-digit number)

18540915305336499736…06633821629617121279

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 86786

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 3ff8e80aa3c48187be577276187808db187682293a26d69325d073f1711769ea

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 #86,786 on Chainz ↗