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Block #82,499

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2013, 11:32:30 AM Β· Difficulty 9.2740 Β· 6,743,912 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f93e832e972e721d06cbd37ce492d0e4a088cd9477668c6a0ce00344d471925e
View on Chainz β†—

Height

#82,499

Difficulty

9.274010

Transactions

1

Size

199 B

Version

2

Bits

09462584

Nonce

182,697

Timestamp

7/25/2013, 11:32:30 AM

Confirmations

6,743,912

Merkle Root

fa89f6158a3095f1bdfb92c2f97aea9272a87be7535d0130b6951d6ea1b3b796
Transactions (1)
Coinbasefa89f6158a3095…951d6ea1b3b796
1 in β†’ 1 out11.6100 XPM109 B
AM9F4hsh…otZwWpXg
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.668 Γ— 10⁹³(94-digit number)
36688081880857150482…29657113484510834000
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.668 Γ— 10⁹³(94-digit number)
36688081880857150482…29657113484510833999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.668 Γ— 10⁹³(94-digit number)
36688081880857150482…29657113484510834001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
7.337 Γ— 10⁹³(94-digit number)
73376163761714300965…59314226969021667999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.337 Γ— 10⁹³(94-digit number)
73376163761714300965…59314226969021668001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.467 Γ— 10⁹⁴(95-digit number)
14675232752342860193…18628453938043335999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.467 Γ— 10⁹⁴(95-digit number)
14675232752342860193…18628453938043336001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.935 Γ— 10⁹⁴(95-digit number)
29350465504685720386…37256907876086671999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.935 Γ— 10⁹⁴(95-digit number)
29350465504685720386…37256907876086672001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
5.870 Γ— 10⁹⁴(95-digit number)
58700931009371440772…74513815752173343999
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 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 82499

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 f93e832e972e721d06cbd37ce492d0e4a088cd9477668c6a0ce00344d471925e

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 β†’ Debug Window β†’ 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 #82,499 on Chainz β†—
Circulating Supply:57,855,420 XPMΒ·at block #6,826,410 Β· updates every 60s
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