XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #473,175

Block #473,175

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/3/2014, 5:31:46 PM Β· Difficulty 10.4464 Β· 6,339,312 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
44c2db40a0ae783d10a9c7dbb397d2d508cf9cbdac9db370f41bc1273aa2d737
View on Chainz β†—

Height

#473,175

Difficulty

10.446383

Transactions

1

Size

201 B

Version

2

Bits

0a724628

Nonce

82,412

Timestamp

4/3/2014, 5:31:46 PM

Confirmations

6,339,312

Merkle Root

128ef26006a7ac06b9ff0602b89c89356711385248a03ba879b0ac41ebafa48b
Transactions (1)
Coinbase128ef26006a7ac…b0ac41ebafa48b
1 in β†’ 1 out9.1500 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.553 Γ— 10⁹⁷(98-digit number)
25532515549359458649…44143934417070295040
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
2.553 Γ— 10⁹⁷(98-digit number)
25532515549359458649…44143934417070295039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.553 Γ— 10⁹⁷(98-digit number)
25532515549359458649…44143934417070295041
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
5.106 Γ— 10⁹⁷(98-digit number)
51065031098718917299…88287868834140590079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.106 Γ— 10⁹⁷(98-digit number)
51065031098718917299…88287868834140590081
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
1.021 Γ— 10⁹⁸(99-digit number)
10213006219743783459…76575737668281180159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.021 Γ— 10⁹⁸(99-digit number)
10213006219743783459…76575737668281180161
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
2.042 Γ— 10⁹⁸(99-digit number)
20426012439487566919…53151475336562360319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.042 Γ— 10⁹⁸(99-digit number)
20426012439487566919…53151475336562360321
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
4.085 Γ— 10⁹⁸(99-digit number)
40852024878975133839…06302950673124720639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.085 Γ— 10⁹⁸(99-digit number)
40852024878975133839…06302950673124720641
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
8.170 Γ— 10⁹⁸(99-digit number)
81704049757950267679…12605901346249441279
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 473175

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 44c2db40a0ae783d10a9c7dbb397d2d508cf9cbdac9db370f41bc1273aa2d737

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 #473,175 on Chainz β†—
Circulating Supply:57,743,925 XPMΒ·at block #6,812,486 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.
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