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Home/Chain Registry/Block #2,585,732

Block #2,585,732

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/26/2018, 12:00:00 AM Β· Difficulty 11.2600 Β· 4,255,605 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a5a0a14fd768529b4f7dceaf964deff0351a622dee97a962e937fa41b3698c86
View on Chainz β†—

Difficulty

11.260049

Transactions

1

Size

200 B

Version

2

Bits

0b42929a

Nonce

2,018,423,146

Timestamp

3/26/2018, 12:00:00 AM

Confirmations

4,255,605

Merkle Root

2f04878821f6236cfa956528352d1f909da478691141115a86ac4586c50af724
Transactions (1)
Coinbase2f04878821f623…ac4586c50af724
1 in β†’ 1 out7.8700 XPM110 B
AdSAh5Eb…KjpwEmwB
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.

3.588 Γ— 10⁹³(94-digit number)
35887234017526417475…49309574680042854400
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
3.588 Γ— 10⁹³(94-digit number)
35887234017526417475…49309574680042854399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.588 Γ— 10⁹³(94-digit number)
35887234017526417475…49309574680042854401
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
7.177 Γ— 10⁹³(94-digit number)
71774468035052834951…98619149360085708799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.177 Γ— 10⁹³(94-digit number)
71774468035052834951…98619149360085708801
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
1.435 Γ— 10⁹⁴(95-digit number)
14354893607010566990…97238298720171417599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.435 Γ— 10⁹⁴(95-digit number)
14354893607010566990…97238298720171417601
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
2.870 Γ— 10⁹⁴(95-digit number)
28709787214021133980…94476597440342835199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.870 Γ— 10⁹⁴(95-digit number)
28709787214021133980…94476597440342835201
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
5.741 Γ— 10⁹⁴(95-digit number)
57419574428042267961…88953194880685670399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.741 Γ— 10⁹⁴(95-digit number)
57419574428042267961…88953194880685670401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.148 Γ— 10⁹⁡(96-digit number)
11483914885608453592…77906389761371340799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2585732

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 a5a0a14fd768529b4f7dceaf964deff0351a622dee97a962e937fa41b3698c86

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 #2,585,732 on Chainz β†—
Circulating Supply:57,975,061 XPMΒ·at block #6,841,336 Β· updates every 60s
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