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Home/Chain Registry/Block #2,683,038

Block #2,683,038

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2018, 1:10:04 PM Β· Difficulty 11.6906 Β· 4,158,143 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
53e97cae4e426e2fd3ae82d28ac94d282ddc290b8d4ef2a0fb22b262f124fa42
View on Chainz β†—

Difficulty

11.690621

Transactions

1

Size

201 B

Version

2

Bits

0bb0cc8f

Nonce

2,043,223,933

Timestamp

5/29/2018, 1:10:04 PM

Confirmations

4,158,143

Merkle Root

d9e9700c0b5620333fd5f90aa8cfd809af63e7ce9f25e066d0ac53b108d70a95
Transactions (1)
Coinbased9e9700c0b5620…ac53b108d70a95
1 in β†’ 1 out7.3000 XPM110 B
AKWDXPje…FtQwW7P2
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.

2.174 Γ— 10⁹⁢(97-digit number)
21746180831354683409…62083915024432304640
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
2.174 Γ— 10⁹⁢(97-digit number)
21746180831354683409…62083915024432304639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.174 Γ— 10⁹⁢(97-digit number)
21746180831354683409…62083915024432304641
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
4.349 Γ— 10⁹⁢(97-digit number)
43492361662709366818…24167830048864609279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.349 Γ— 10⁹⁢(97-digit number)
43492361662709366818…24167830048864609281
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
8.698 Γ— 10⁹⁢(97-digit number)
86984723325418733637…48335660097729218559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.698 Γ— 10⁹⁢(97-digit number)
86984723325418733637…48335660097729218561
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
1.739 Γ— 10⁹⁷(98-digit number)
17396944665083746727…96671320195458437119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.739 Γ— 10⁹⁷(98-digit number)
17396944665083746727…96671320195458437121
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
3.479 Γ— 10⁹⁷(98-digit number)
34793889330167493455…93342640390916874239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.479 Γ— 10⁹⁷(98-digit number)
34793889330167493455…93342640390916874241
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
6.958 Γ— 10⁹⁷(98-digit number)
69587778660334986910…86685280781833748479
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 2683038

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 53e97cae4e426e2fd3ae82d28ac94d282ddc290b8d4ef2a0fb22b262f124fa42

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 #2,683,038 on Chainz β†—
Circulating Supply:57,973,807 XPMΒ·at block #6,841,180 Β· updates every 60s
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