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Home/Chain Registry/Block #2,169,822

Block #2,169,822

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2017, 3:49:38 AM Β· Difficulty 10.9007 Β· 4,673,123 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
75fea8de52ef44105dd9cf7af814e22e78a5fbc988a2c4004f254ed82bae2a6a
View on Chainz β†—

Difficulty

10.900695

Transactions

2

Size

425 B

Version

2

Bits

0ae693f9

Nonce

559,784,845

Timestamp

6/21/2017, 3:49:38 AM

Confirmations

4,673,123

Merkle Root

efb6bbaa01963c6b65c8fea5d1ab1b002d509fcb682145cd252bc2df622a0490
Transactions (2)
Coinbase278d1212160d78…9ba5cde56f0a15
1 in β†’ 1 out8.4100 XPM109 B
AP5exmzc…F9Y8LM3F
ed932dcc2fc5c8…2fd088d752b4f6
1 in β†’ 2 out144450.2611 XPM226 B
AGob44z6…h4GzFLTiAaZoWCHB…mjEezUPQ
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.

4.622 Γ— 10⁹⁴(95-digit number)
46220095164387508237…83663400865142574000
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
4.622 Γ— 10⁹⁴(95-digit number)
46220095164387508237…83663400865142573999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.622 Γ— 10⁹⁴(95-digit number)
46220095164387508237…83663400865142574001
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
9.244 Γ— 10⁹⁴(95-digit number)
92440190328775016475…67326801730285147999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.244 Γ— 10⁹⁴(95-digit number)
92440190328775016475…67326801730285148001
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
1.848 Γ— 10⁹⁡(96-digit number)
18488038065755003295…34653603460570295999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.848 Γ— 10⁹⁡(96-digit number)
18488038065755003295…34653603460570296001
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
3.697 Γ— 10⁹⁡(96-digit number)
36976076131510006590…69307206921140591999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.697 Γ— 10⁹⁡(96-digit number)
36976076131510006590…69307206921140592001
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
7.395 Γ— 10⁹⁡(96-digit number)
73952152263020013180…38614413842281183999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.395 Γ— 10⁹⁡(96-digit number)
73952152263020013180…38614413842281184001
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
1.479 Γ— 10⁹⁢(97-digit number)
14790430452604002636…77228827684562367999
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 2169822

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 75fea8de52ef44105dd9cf7af814e22e78a5fbc988a2c4004f254ed82bae2a6a

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 #2,169,822 on Chainz β†—
Circulating Supply:57,987,911 XPMΒ·at block #6,842,944 Β· updates every 60s
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