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Home/Chain Registry/Block #2,213,407

Block #2,213,407

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2017, 12:07:04 PM Β· Difficulty 10.9439 Β· 4,624,624 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
05e317387529d775fb120f128ddb32ee463c4140b30a2216e3a336427da40a28
View on Chainz β†—

Difficulty

10.943948

Transactions

1

Size

199 B

Version

2

Bits

0af1a697

Nonce

2,103,569,389

Timestamp

7/19/2017, 12:07:04 PM

Confirmations

4,624,624

Merkle Root

3f83d8a28ececdcf789b9cb0154ebab78ae31a365b85a7d0cc81790cac928da5
Transactions (1)
Coinbase3f83d8a28ececd…81790cac928da5
1 in β†’ 1 out8.3400 XPM109 B
Acwca1LN…vH1wB8D6
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.

8.868 Γ— 10⁹⁡(96-digit number)
88682319264308956126…76681858531261747200
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
8.868 Γ— 10⁹⁡(96-digit number)
88682319264308956126…76681858531261747199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.868 Γ— 10⁹⁡(96-digit number)
88682319264308956126…76681858531261747201
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
1.773 Γ— 10⁹⁢(97-digit number)
17736463852861791225…53363717062523494399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.773 Γ— 10⁹⁢(97-digit number)
17736463852861791225…53363717062523494401
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
3.547 Γ— 10⁹⁢(97-digit number)
35472927705723582450…06727434125046988799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.547 Γ— 10⁹⁢(97-digit number)
35472927705723582450…06727434125046988801
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
7.094 Γ— 10⁹⁢(97-digit number)
70945855411447164900…13454868250093977599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.094 Γ— 10⁹⁢(97-digit number)
70945855411447164900…13454868250093977601
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
1.418 Γ— 10⁹⁷(98-digit number)
14189171082289432980…26909736500187955199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.418 Γ— 10⁹⁷(98-digit number)
14189171082289432980…26909736500187955201
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
2.837 Γ— 10⁹⁷(98-digit number)
28378342164578865960…53819473000375910399
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 2213407

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 05e317387529d775fb120f128ddb32ee463c4140b30a2216e3a336427da40a28

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 #2,213,407 on Chainz β†—
Circulating Supply:57,948,598 XPMΒ·at block #6,838,030 Β· updates every 60s
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