XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #204,599

Block #204,599

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/11/2013, 2:46:51 PM Β· Difficulty 9.8987 Β· 6,610,224 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c0baf2dd84e2de58f65721e5267de8236e5519660c4a1d1b4025d2fd22378cb6
View on Chainz β†—

Height

#204,599

Difficulty

9.898712

Transactions

2

Size

540 B

Version

2

Bits

09e611ff

Nonce

67,230

Timestamp

10/11/2013, 2:46:51 PM

Confirmations

6,610,224

Merkle Root

1236b957863f8b0abc0c08eaeebc057966c7a5b8fb0f86cd1aeee5af89070ef9
Transactions (2)
Coinbased312d858fd62a6…9e14c16d1a6079
1 in β†’ 1 out10.2000 XPM110 B
ANvtpRa1…QjsraDJz
2b127d3de7a589…d36278be05325d
2 in β†’ 1 out166.6364 XPM339 B
AJgBPut6…WpPNbWNL
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.

4.573 Γ— 10⁹⁷(98-digit number)
45736505936545010830…23505789078091561040
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
4.573 Γ— 10⁹⁷(98-digit number)
45736505936545010830…23505789078091561039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.573 Γ— 10⁹⁷(98-digit number)
45736505936545010830…23505789078091561041
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
9.147 Γ— 10⁹⁷(98-digit number)
91473011873090021661…47011578156183122079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.147 Γ— 10⁹⁷(98-digit number)
91473011873090021661…47011578156183122081
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
1.829 Γ— 10⁹⁸(99-digit number)
18294602374618004332…94023156312366244159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.829 Γ— 10⁹⁸(99-digit number)
18294602374618004332…94023156312366244161
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
3.658 Γ— 10⁹⁸(99-digit number)
36589204749236008664…88046312624732488319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.658 Γ— 10⁹⁸(99-digit number)
36589204749236008664…88046312624732488321
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
7.317 Γ— 10⁹⁸(99-digit number)
73178409498472017329…76092625249464976639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 204599

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 c0baf2dd84e2de58f65721e5267de8236e5519660c4a1d1b4025d2fd22378cb6

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 #204,599 on Chainz β†—
Circulating Supply:57,762,672 XPMΒ·at block #6,814,822 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy