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Home/Chain Registry/Block #2,829,595

Block #2,829,595

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2018, 2:27:15 AM Β· Difficulty 11.7140 Β· 4,012,307 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9980bd76b1053d6ea55d448449002a24b098b788a9330d1e500fa07a99807326
View on Chainz β†—

Difficulty

11.713955

Transactions

1

Size

201 B

Version

2

Bits

0bb6c5c6

Nonce

1,667,488,323

Timestamp

9/8/2018, 2:27:15 AM

Confirmations

4,012,307

Merkle Root

7609acaf5014df091add5bdbe48c9b611c0291db5fd93f98c8d8b4a176fefcfb
Transactions (1)
Coinbase7609acaf5014df…d8b4a176fefcfb
1 in β†’ 1 out7.2800 XPM110 B
AW4PriNs…26wStccf
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.

1.100 Γ— 10⁹⁸(99-digit number)
11009724491531292828…05512356788155637760
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
1.100 Γ— 10⁹⁸(99-digit number)
11009724491531292828…05512356788155637759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.100 Γ— 10⁹⁸(99-digit number)
11009724491531292828…05512356788155637761
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
2.201 Γ— 10⁹⁸(99-digit number)
22019448983062585656…11024713576311275519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.201 Γ— 10⁹⁸(99-digit number)
22019448983062585656…11024713576311275521
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
4.403 Γ— 10⁹⁸(99-digit number)
44038897966125171313…22049427152622551039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.403 Γ— 10⁹⁸(99-digit number)
44038897966125171313…22049427152622551041
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
8.807 Γ— 10⁹⁸(99-digit number)
88077795932250342627…44098854305245102079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.807 Γ— 10⁹⁸(99-digit number)
88077795932250342627…44098854305245102081
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
1.761 Γ— 10⁹⁹(100-digit number)
17615559186450068525…88197708610490204159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.761 Γ— 10⁹⁹(100-digit number)
17615559186450068525…88197708610490204161
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
3.523 Γ— 10⁹⁹(100-digit number)
35231118372900137050…76395417220980408319
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 2829595

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 9980bd76b1053d6ea55d448449002a24b098b788a9330d1e500fa07a99807326

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 #2,829,595 on Chainz β†—
Circulating Supply:57,979,589 XPMΒ·at block #6,841,901 Β· updates every 60s
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