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Block #46,443

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2013, 6:34:10 AM Β· Difficulty 8.7923 Β· 6,760,744 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
416a83988497f6c809dd8a85ef3bf2dbb96789df2f0c1277347884339da42aca
View on Chainz β†—

Height

#46,443

Difficulty

8.792255

Transactions

2

Size

357 B

Version

2

Bits

08cad13d

Nonce

664

Timestamp

7/15/2013, 6:34:10 AM

Confirmations

6,760,744

Merkle Root

52d0426c312f4268b39be6c57f8522ab8ee9ee83a40c1188751d364aae27371f
Transactions (2)
Coinbased4499cf186fecc…192b47f9089f47
1 in β†’ 1 out12.9300 XPM110 B
AZL9DFFi…mwQY3vsF
856b7875673d78…033355e009352a
1 in β†’ 1 out13.3300 XPM157 B
ANBXgfaf…ZXqNYSdt
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.

7.452 Γ— 10⁹⁴(95-digit number)
74529962623988639499…67901505263321429020
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
7.452 Γ— 10⁹⁴(95-digit number)
74529962623988639499…67901505263321429019
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.452 Γ— 10⁹⁴(95-digit number)
74529962623988639499…67901505263321429021
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
1.490 Γ— 10⁹⁡(96-digit number)
14905992524797727899…35803010526642858039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.490 Γ— 10⁹⁡(96-digit number)
14905992524797727899…35803010526642858041
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
2.981 Γ— 10⁹⁡(96-digit number)
29811985049595455799…71606021053285716079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.981 Γ— 10⁹⁡(96-digit number)
29811985049595455799…71606021053285716081
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
5.962 Γ— 10⁹⁡(96-digit number)
59623970099190911599…43212042106571432159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.962 Γ— 10⁹⁡(96-digit number)
59623970099190911599…43212042106571432161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8
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 46443

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 416a83988497f6c809dd8a85ef3bf2dbb96789df2f0c1277347884339da42aca

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 #46,443 on Chainz β†—
Circulating Supply:57,701,508 XPMΒ·at block #6,807,186 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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