Home/Chain Registry/Block #81,300

Block #81,300

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 4:05:03 PM · Difficulty 9.2693 · 6,710,064 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d12ffc95c2040d973017a0c88a05138821318ef04823dfd37ca0564929c305a

View on Chainz ↗

Height

#81,300

Difficulty

9.269276

Transactions

Size

728 B

Version

Bits

0944ef47

Nonce

317

Timestamp

7/24/2013, 4:05:03 PM

Confirmations

6,710,064

Merkle Root

2ff1c772cb995b1dd044641b4a19bbdef6b0c66e140abbde9bff68df08d89f5e

Transactions (2)

Coinbase5f8513c08b8bde…a80507123484d6

1 in → 1 out11.6300 XPM109 B

AMXfVMdW…u1Br1tGN

c6d13d9ff0b946…62bf4f6e855835

3 in → 2 out150.7058 XPM521 B

AYNVxcFF…yy7Lr1Rb ASEGjn4e…ebEaC7Rb

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.

1.199 × 10¹¹³(114-digit number)

11998200722623420321…88934487179277204780

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

1.199 × 10¹¹³(114-digit number)

11998200722623420321…88934487179277204779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.199 × 10¹¹³(114-digit number)

11998200722623420321…88934487179277204781

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

2.399 × 10¹¹³(114-digit number)

23996401445246840642…77868974358554409559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.399 × 10¹¹³(114-digit number)

23996401445246840642…77868974358554409561

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

4.799 × 10¹¹³(114-digit number)

47992802890493681285…55737948717108819119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.799 × 10¹¹³(114-digit number)

47992802890493681285…55737948717108819121

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

9.598 × 10¹¹³(114-digit number)

95985605780987362571…11475897434217638239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.598 × 10¹¹³(114-digit number)

95985605780987362571…11475897434217638241

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

1.919 × 10¹¹⁴(115-digit number)

19197121156197472514…22951794868435276479

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 81300

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 5d12ffc95c2040d973017a0c88a05138821318ef04823dfd37ca0564929c305a

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 #81,300 on Chainz ↗