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Block #489,357

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/13/2014, 6:02:02 AM Β· Difficulty 10.6648 Β· 6,337,212 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7cd2001957ee4f7ca663a2d79a9fc12b0a125d814f9f96002085b220693b2a2c
View on Chainz β†—

Height

#489,357

Difficulty

10.664815

Transactions

1

Size

200 B

Version

2

Bits

0aaa3152

Nonce

22,608

Timestamp

4/13/2014, 6:02:02 AM

Confirmations

6,337,212

Merkle Root

d8bab8fe658b9fdbdc96de5ac212b9f8f45b04b6887a053ec6b16a46dd142c68
Transactions (1)
Coinbased8bab8fe658b9f…b16a46dd142c68
1 in β†’ 1 out8.7800 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.

5.428 Γ— 10⁹⁡(96-digit number)
54289870277422488139…21690952985821980400
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
5.428 Γ— 10⁹⁡(96-digit number)
54289870277422488139…21690952985821980399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.428 Γ— 10⁹⁡(96-digit number)
54289870277422488139…21690952985821980401
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
1.085 Γ— 10⁹⁢(97-digit number)
10857974055484497627…43381905971643960799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.085 Γ— 10⁹⁢(97-digit number)
10857974055484497627…43381905971643960801
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
2.171 Γ— 10⁹⁢(97-digit number)
21715948110968995255…86763811943287921599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.171 Γ— 10⁹⁢(97-digit number)
21715948110968995255…86763811943287921601
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
4.343 Γ— 10⁹⁢(97-digit number)
43431896221937990511…73527623886575843199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.343 Γ— 10⁹⁢(97-digit number)
43431896221937990511…73527623886575843201
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
8.686 Γ— 10⁹⁢(97-digit number)
86863792443875981022…47055247773151686399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.686 Γ— 10⁹⁢(97-digit number)
86863792443875981022…47055247773151686401
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
1.737 Γ— 10⁹⁷(98-digit number)
17372758488775196204…94110495546303372799
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 489357

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 7cd2001957ee4f7ca663a2d79a9fc12b0a125d814f9f96002085b220693b2a2c

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 #489,357 on Chainz β†—
Circulating Supply:57,856,703 XPMΒ·at block #6,826,568 Β· updates every 60s
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