Home/Chain Registry/Block #86,300

Block #86,300

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 1:09:03 AM · Difficulty 9.2892 · 6,703,736 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

924fb958065cd91da61f98d375e08674d2341318c6db4113a2d3f21c292c4009

View on Chainz ↗

Height

#86,300

Difficulty

9.289176

Transactions

Size

209 B

Version

Bits

094a0775

Nonce

179

Timestamp

7/28/2013, 1:09:03 AM

Confirmations

6,703,736

Merkle Root

5c3b9b1db0a55c18a6ab418b0ac34b86cfdae40701f2365def33334c678ec07c

Transactions (1)

Coinbase5c3b9b1db0a55c…33334c678ec07c

1 in → 1 out11.5700 XPM110 B

AcgU9guA…qx4YHY9h

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.

7.336 × 10¹¹⁵(116-digit number)

73361501752134685448…96884531169239774370

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

7.336 × 10¹¹⁵(116-digit number)

73361501752134685448…96884531169239774369

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.336 × 10¹¹⁵(116-digit number)

73361501752134685448…96884531169239774371

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

1.467 × 10¹¹⁶(117-digit number)

14672300350426937089…93769062338479548739

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.467 × 10¹¹⁶(117-digit number)

14672300350426937089…93769062338479548741

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

2.934 × 10¹¹⁶(117-digit number)

29344600700853874179…87538124676959097479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.934 × 10¹¹⁶(117-digit number)

29344600700853874179…87538124676959097481

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

5.868 × 10¹¹⁶(117-digit number)

58689201401707748358…75076249353918194959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.868 × 10¹¹⁶(117-digit number)

58689201401707748358…75076249353918194961

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

1.173 × 10¹¹⁷(118-digit number)

11737840280341549671…50152498707836389919

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 86300

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 924fb958065cd91da61f98d375e08674d2341318c6db4113a2d3f21c292c4009

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 #86,300 on Chainz ↗