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Block #2,580,267

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/23/2018, 3:04:38 AM Β· Difficulty 11.0364 Β· 4,256,743 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e860a4b7ded0bb1564fd9dcaeb2196549db496e87d961bdcdc7cfc3e50f66f13
View on Chainz β†—

Difficulty

11.036377

Transactions

1

Size

201 B

Version

2

Bits

0b095007

Nonce

478,810,109

Timestamp

3/23/2018, 3:04:38 AM

Confirmations

4,256,743

Merkle Root

8893ca1059a98b67440e5bdd48421f0dadc0f5bd4b960ce527ffbd5e6e9bd1ae
Transactions (1)
Coinbase8893ca1059a98b…ffbd5e6e9bd1ae
1 in β†’ 1 out8.2000 XPM110 B
AKMTCDMC…ZxDGsex1
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.

1.421 Γ— 10⁹⁢(97-digit number)
14217168690416851195…92521682434846586880
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
1.421 Γ— 10⁹⁢(97-digit number)
14217168690416851195…92521682434846586879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.421 Γ— 10⁹⁢(97-digit number)
14217168690416851195…92521682434846586881
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
2.843 Γ— 10⁹⁢(97-digit number)
28434337380833702390…85043364869693173759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.843 Γ— 10⁹⁢(97-digit number)
28434337380833702390…85043364869693173761
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
5.686 Γ— 10⁹⁢(97-digit number)
56868674761667404780…70086729739386347519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.686 Γ— 10⁹⁢(97-digit number)
56868674761667404780…70086729739386347521
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
1.137 Γ— 10⁹⁷(98-digit number)
11373734952333480956…40173459478772695039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.137 Γ— 10⁹⁷(98-digit number)
11373734952333480956…40173459478772695041
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
2.274 Γ— 10⁹⁷(98-digit number)
22747469904666961912…80346918957545390079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.274 Γ— 10⁹⁷(98-digit number)
22747469904666961912…80346918957545390081
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
4.549 Γ— 10⁹⁷(98-digit number)
45494939809333923824…60693837915090780159
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 2580267

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 e860a4b7ded0bb1564fd9dcaeb2196549db496e87d961bdcdc7cfc3e50f66f13

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 #2,580,267 on Chainz β†—
Circulating Supply:57,940,376 XPMΒ·at block #6,837,009 Β· updates every 60s
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