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Block #436,383

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/9/2014, 1:42:51 PM Β· Difficulty 10.3588 Β· 6,368,749 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
241afb305facbaba96c943664ee21b8d4deeaf17a8fb5dfd23f3ff661dda6774
View on Chainz β†—

Height

#436,383

Difficulty

10.358778

Transactions

1

Size

200 B

Version

2

Bits

0a5bd8df

Nonce

565,324

Timestamp

3/9/2014, 1:42:51 PM

Confirmations

6,368,749

Merkle Root

a72739d59d4e3509ae728e7b6f2d1c02a29a770470e8fa74c23cd3e1ab32ccb8
Transactions (1)
Coinbasea72739d59d4e35…3cd3e1ab32ccb8
1 in β†’ 1 out9.3000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

4.581 Γ— 10⁹⁴(95-digit number)
45810188825338221404…58588306668862181760
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
4.581 Γ— 10⁹⁴(95-digit number)
45810188825338221404…58588306668862181759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.581 Γ— 10⁹⁴(95-digit number)
45810188825338221404…58588306668862181761
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
9.162 Γ— 10⁹⁴(95-digit number)
91620377650676442809…17176613337724363519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.162 Γ— 10⁹⁴(95-digit number)
91620377650676442809…17176613337724363521
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
1.832 Γ— 10⁹⁡(96-digit number)
18324075530135288561…34353226675448727039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.832 Γ— 10⁹⁡(96-digit number)
18324075530135288561…34353226675448727041
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
3.664 Γ— 10⁹⁡(96-digit number)
36648151060270577123…68706453350897454079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.664 Γ— 10⁹⁡(96-digit number)
36648151060270577123…68706453350897454081
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
7.329 Γ— 10⁹⁡(96-digit number)
73296302120541154247…37412906701794908159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.329 Γ— 10⁹⁡(96-digit number)
73296302120541154247…37412906701794908161
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 436383

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 241afb305facbaba96c943664ee21b8d4deeaf17a8fb5dfd23f3ff661dda6774

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 #436,383 on Chainz β†—
Circulating Supply:57,685,120 XPMΒ·at block #6,805,131 Β· updates every 60s
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