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Home/Chain Registry/Block #2,799,779

Block #2,799,779

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/18/2018, 8:04:59 PM Β· Difficulty 11.6746 Β· 4,043,511 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
47a54eb22c844b0dbb6577ea38e1a4872a0fddc08cf77908c9607746755921ad
View on Chainz β†—

Difficulty

11.674571

Transactions

1

Size

201 B

Version

2

Bits

0bacb0b2

Nonce

326,065,263

Timestamp

8/18/2018, 8:04:59 PM

Confirmations

4,043,511

Merkle Root

c6a7680e1156d9bf38c7e8243c6957306748faeb37b5f099bad849f122e5a22c
Transactions (1)
Coinbasec6a7680e1156d9…d849f122e5a22c
1 in β†’ 1 out7.3200 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.864 Γ— 10⁹⁷(98-digit number)
28645482256167755345…43091294392887541760
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
2.864 Γ— 10⁹⁷(98-digit number)
28645482256167755345…43091294392887541759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.864 Γ— 10⁹⁷(98-digit number)
28645482256167755345…43091294392887541761
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
5.729 Γ— 10⁹⁷(98-digit number)
57290964512335510690…86182588785775083519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.729 Γ— 10⁹⁷(98-digit number)
57290964512335510690…86182588785775083521
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
1.145 Γ— 10⁹⁸(99-digit number)
11458192902467102138…72365177571550167039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.145 Γ— 10⁹⁸(99-digit number)
11458192902467102138…72365177571550167041
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
2.291 Γ— 10⁹⁸(99-digit number)
22916385804934204276…44730355143100334079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.291 Γ— 10⁹⁸(99-digit number)
22916385804934204276…44730355143100334081
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
4.583 Γ— 10⁹⁸(99-digit number)
45832771609868408552…89460710286200668159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.583 Γ— 10⁹⁸(99-digit number)
45832771609868408552…89460710286200668161
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
9.166 Γ— 10⁹⁸(99-digit number)
91665543219736817104…78921420572401336319
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 2799779

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 47a54eb22c844b0dbb6577ea38e1a4872a0fddc08cf77908c9607746755921ad

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 #2,799,779 on Chainz β†—
Circulating Supply:57,990,684 XPMΒ·at block #6,843,289 Β· updates every 60s
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