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Home/Chain Registry/Block #2,651,883

Block #2,651,883

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/7/2018, 4:23:00 AM Β· Difficulty 11.7481 Β· 4,184,788 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
efcb9a97d767a32c100c5d6e6a7f575d79f5b3fa865acfe8c594cb7f5ac29751
View on Chainz β†—

Difficulty

11.748070

Transactions

3

Size

2.26 KB

Version

2

Bits

0bbf8183

Nonce

1,835,267,803

Timestamp

5/7/2018, 4:23:00 AM

Confirmations

4,184,788

Merkle Root

18d7ef501adc1926e0265962359bb99f0470a0400327449cf53b5efdecf4a161
Transactions (3)
Coinbasec5a6badb83ce37…4f7026dbabf03e
1 in β†’ 1 out7.2600 XPM110 B
AP1GjvSh…eDiZWJF8
fef1a48e682a79…c99f32367ce3e0
13 in β†’ 1 out80.0000 XPM1.56 KB
AXnoW1rM…Jk3oGQx6
86bf41bf830b28…16fde6933167d6
3 in β†’ 2 out4.0900 XPM520 B
AUo7p97H…sJ9AyoTaAZYfjakE…5RJniivm
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.

2.182 Γ— 10⁹⁢(97-digit number)
21829338057659593861…31626400496054650880
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
2.182 Γ— 10⁹⁢(97-digit number)
21829338057659593861…31626400496054650879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.182 Γ— 10⁹⁢(97-digit number)
21829338057659593861…31626400496054650881
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
4.365 Γ— 10⁹⁢(97-digit number)
43658676115319187723…63252800992109301759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.365 Γ— 10⁹⁢(97-digit number)
43658676115319187723…63252800992109301761
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
8.731 Γ— 10⁹⁢(97-digit number)
87317352230638375446…26505601984218603519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.731 Γ— 10⁹⁢(97-digit number)
87317352230638375446…26505601984218603521
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
1.746 Γ— 10⁹⁷(98-digit number)
17463470446127675089…53011203968437207039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.746 Γ— 10⁹⁷(98-digit number)
17463470446127675089…53011203968437207041
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
3.492 Γ— 10⁹⁷(98-digit number)
34926940892255350178…06022407936874414079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.492 Γ— 10⁹⁷(98-digit number)
34926940892255350178…06022407936874414081
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
6.985 Γ— 10⁹⁷(98-digit number)
69853881784510700357…12044815873748828159
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 2651883

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 efcb9a97d767a32c100c5d6e6a7f575d79f5b3fa865acfe8c594cb7f5ac29751

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 #2,651,883 on Chainz β†—
Circulating Supply:57,937,647 XPMΒ·at block #6,836,670 Β· updates every 60s
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