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Home/Chain Registry/Block #2,832,971

Block #2,832,971

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 10:23:16 AM Β· Difficulty 11.7152 Β· 4,010,059 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4051ba7b0fb63c0daea098524e9df38b40f8947aee413390556eaa59b3473127
View on Chainz β†—

Difficulty

11.715219

Transactions

1

Size

201 B

Version

2

Bits

0bb71894

Nonce

578,624,828

Timestamp

9/10/2018, 10:23:16 AM

Confirmations

4,010,059

Merkle Root

f92629109e049655711bdaa794b0edc0b700ba9a43a7a91a4eeac6c30aff6c3d
Transactions (1)
Coinbasef92629109e0496…eac6c30aff6c3d
1 in β†’ 1 out7.2700 XPM110 B
AcSLaumM…Sw4MgGUU
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.

5.053 Γ— 10⁹⁢(97-digit number)
50533235640271759418…28489796867777454080
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
5.053 Γ— 10⁹⁢(97-digit number)
50533235640271759418…28489796867777454079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.053 Γ— 10⁹⁢(97-digit number)
50533235640271759418…28489796867777454081
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
1.010 Γ— 10⁹⁷(98-digit number)
10106647128054351883…56979593735554908159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.010 Γ— 10⁹⁷(98-digit number)
10106647128054351883…56979593735554908161
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
2.021 Γ— 10⁹⁷(98-digit number)
20213294256108703767…13959187471109816319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.021 Γ— 10⁹⁷(98-digit number)
20213294256108703767…13959187471109816321
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
4.042 Γ— 10⁹⁷(98-digit number)
40426588512217407534…27918374942219632639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.042 Γ— 10⁹⁷(98-digit number)
40426588512217407534…27918374942219632641
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
8.085 Γ— 10⁹⁷(98-digit number)
80853177024434815069…55836749884439265279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.085 Γ— 10⁹⁷(98-digit number)
80853177024434815069…55836749884439265281
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
1.617 Γ— 10⁹⁸(99-digit number)
16170635404886963013…11673499768878530559
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 2832971

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 4051ba7b0fb63c0daea098524e9df38b40f8947aee413390556eaa59b3473127

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 #2,832,971 on Chainz β†—
Circulating Supply:57,988,595 XPMΒ·at block #6,843,029 Β· updates every 60s
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