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Home/Chain Registry/Block #2,815,433

Block #2,815,433

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2018, 2:49:35 PM Β· Difficulty 11.6833 Β· 4,024,245 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
de78873298821c9eda65df9fe27c3d3b1c35577ff0a73301becf9df56583b7dc
View on Chainz β†—

Difficulty

11.683345

Transactions

1

Size

202 B

Version

2

Bits

0baeefba

Nonce

881,839,138

Timestamp

8/29/2018, 2:49:35 PM

Confirmations

4,024,245

Merkle Root

c32a14aaec3275bbb96fe170d679a9af897105fb8a5a31e312fd8d093d2aa973
Transactions (1)
Coinbasec32a14aaec3275…fd8d093d2aa973
1 in β†’ 1 out7.3100 XPM110 B
AHLPfD14…QqL4XMxD
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.

1.039 Γ— 10⁹⁹(100-digit number)
10398339407735766346…42109441962020700160
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
1.039 Γ— 10⁹⁹(100-digit number)
10398339407735766346…42109441962020700159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.039 Γ— 10⁹⁹(100-digit number)
10398339407735766346…42109441962020700161
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
2.079 Γ— 10⁹⁹(100-digit number)
20796678815471532692…84218883924041400319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.079 Γ— 10⁹⁹(100-digit number)
20796678815471532692…84218883924041400321
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
4.159 Γ— 10⁹⁹(100-digit number)
41593357630943065385…68437767848082800639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.159 Γ— 10⁹⁹(100-digit number)
41593357630943065385…68437767848082800641
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
8.318 Γ— 10⁹⁹(100-digit number)
83186715261886130771…36875535696165601279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.318 Γ— 10⁹⁹(100-digit number)
83186715261886130771…36875535696165601281
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
1.663 Γ— 10¹⁰⁰(101-digit number)
16637343052377226154…73751071392331202559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.663 Γ— 10¹⁰⁰(101-digit number)
16637343052377226154…73751071392331202561
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
3.327 Γ— 10¹⁰⁰(101-digit number)
33274686104754452308…47502142784662405119
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 2815433

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 de78873298821c9eda65df9fe27c3d3b1c35577ff0a73301becf9df56583b7dc

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 #2,815,433 on Chainz β†—
Circulating Supply:57,961,712 XPMΒ·at block #6,839,677 Β· updates every 60s
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