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Home/Chain Registry/Block #2,841,796

Block #2,841,796

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 9/16/2018, 11:41:41 AM Β· Difficulty 11.7214 Β· 4,003,853 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5529c713d888d33e32d45613c0737c53666f18e974b0a2a1f951b5ace2ba24ca
View on Chainz β†—

Difficulty

11.721447

Transactions

1

Size

200 B

Version

2

Bits

0bb8b0bb

Nonce

70,576,809

Timestamp

9/16/2018, 11:41:41 AM

Confirmations

4,003,853

Merkle Root

8a9cfa1fa4d494d3d638df96cdd3a403305ded8cf853107e2dba54893637a697
Transactions (1)
Coinbase8a9cfa1fa4d494…ba54893637a697
1 in β†’ 1 out7.2700 XPM110 B
APUShfBN…HEptQDER
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.

4.237 Γ— 10⁹⁡(96-digit number)
42374197151800770978…97162817687796236720
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
4.237 Γ— 10⁹⁡(96-digit number)
42374197151800770978…97162817687796236719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.237 Γ— 10⁹⁡(96-digit number)
42374197151800770978…97162817687796236721
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
8.474 Γ— 10⁹⁡(96-digit number)
84748394303601541956…94325635375592473439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.474 Γ— 10⁹⁡(96-digit number)
84748394303601541956…94325635375592473441
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
1.694 Γ— 10⁹⁢(97-digit number)
16949678860720308391…88651270751184946879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.694 Γ— 10⁹⁢(97-digit number)
16949678860720308391…88651270751184946881
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
3.389 Γ— 10⁹⁢(97-digit number)
33899357721440616782…77302541502369893759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.389 Γ— 10⁹⁢(97-digit number)
33899357721440616782…77302541502369893761
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
6.779 Γ— 10⁹⁢(97-digit number)
67798715442881233564…54605083004739787519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.779 Γ— 10⁹⁢(97-digit number)
67798715442881233564…54605083004739787521
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
1.355 Γ— 10⁹⁷(98-digit number)
13559743088576246712…09210166009479575039
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.355 Γ— 10⁹⁷(98-digit number)
13559743088576246712…09210166009479575041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2841796

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 5529c713d888d33e32d45613c0737c53666f18e974b0a2a1f951b5ace2ba24ca

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 #2,841,796 on Chainz β†—
Circulating Supply:58,009,641 XPMΒ·at block #6,845,648 Β· updates every 60s
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