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Block #458,207

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/24/2014, 10:29:50 AM Β· Difficulty 10.4214 Β· 6,367,949 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f0f2e0704705c59c9c5bec9162de8269d2401dbffaf62dea6480334a5de804c6
View on Chainz β†—

Height

#458,207

Difficulty

10.421418

Transactions

1

Size

202 B

Version

2

Bits

0a6be20b

Nonce

87,988

Timestamp

3/24/2014, 10:29:50 AM

Confirmations

6,367,949

Merkle Root

254467fd13e213fb82752886e24f2727e192aeb6ccb1bee2a8aef7f9cfe1e403
Transactions (1)
Coinbase254467fd13e213…aef7f9cfe1e403
1 in β†’ 1 out9.1900 XPM110 B
AbYM1Baf…jFZ7mXyo
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.

1.941 Γ— 10⁹⁹(100-digit number)
19419226234488380846…81516514119146396800
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
1.941 Γ— 10⁹⁹(100-digit number)
19419226234488380846…81516514119146396799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.941 Γ— 10⁹⁹(100-digit number)
19419226234488380846…81516514119146396801
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
3.883 Γ— 10⁹⁹(100-digit number)
38838452468976761692…63033028238292793599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.883 Γ— 10⁹⁹(100-digit number)
38838452468976761692…63033028238292793601
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
7.767 Γ— 10⁹⁹(100-digit number)
77676904937953523384…26066056476585587199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.767 Γ— 10⁹⁹(100-digit number)
77676904937953523384…26066056476585587201
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
1.553 Γ— 10¹⁰⁰(101-digit number)
15535380987590704676…52132112953171174399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.553 Γ— 10¹⁰⁰(101-digit number)
15535380987590704676…52132112953171174401
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
3.107 Γ— 10¹⁰⁰(101-digit number)
31070761975181409353…04264225906342348799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.107 Γ— 10¹⁰⁰(101-digit number)
31070761975181409353…04264225906342348801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 458207

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 f0f2e0704705c59c9c5bec9162de8269d2401dbffaf62dea6480334a5de804c6

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 #458,207 on Chainz β†—
Circulating Supply:57,853,374 XPMΒ·at block #6,826,155 Β· updates every 60s
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