XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #470,771

Block #470,771

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/2/2014, 3:57:38 AM Β· Difficulty 10.4287 Β· 6,329,687 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d394b8eafa574855db419e82df8c06f5f54cacd8564458c724c6e5b847f481a
View on Chainz β†—

Height

#470,771

Difficulty

10.428671

Transactions

1

Size

207 B

Version

2

Bits

0a6dbd62

Nonce

104,704

Timestamp

4/2/2014, 3:57:38 AM

Confirmations

6,329,687

Merkle Root

7d38aac5bc0f8bbec3e701da00e7aea8b5a7e504c7ec93ee1633b4398cf5b4db
Transactions (1)
Coinbase7d38aac5bc0f8b…33b4398cf5b4db
1 in β†’ 1 out9.1800 XPM116 B
AbwWkWZt…kawDhufa
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.

5.592 Γ— 10⁹⁷(98-digit number)
55929342948817183747…82082871128537480920
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
5.592 Γ— 10⁹⁷(98-digit number)
55929342948817183747…82082871128537480919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.592 Γ— 10⁹⁷(98-digit number)
55929342948817183747…82082871128537480921
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
1.118 Γ— 10⁹⁸(99-digit number)
11185868589763436749…64165742257074961839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.118 Γ— 10⁹⁸(99-digit number)
11185868589763436749…64165742257074961841
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
2.237 Γ— 10⁹⁸(99-digit number)
22371737179526873499…28331484514149923679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.237 Γ— 10⁹⁸(99-digit number)
22371737179526873499…28331484514149923681
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
4.474 Γ— 10⁹⁸(99-digit number)
44743474359053746998…56662969028299847359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.474 Γ— 10⁹⁸(99-digit number)
44743474359053746998…56662969028299847361
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
8.948 Γ— 10⁹⁸(99-digit number)
89486948718107493996…13325938056599694719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.948 Γ— 10⁹⁸(99-digit number)
89486948718107493996…13325938056599694721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 470771

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 4d394b8eafa574855db419e82df8c06f5f54cacd8564458c724c6e5b847f481a

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 #470,771 on Chainz β†—
Circulating Supply:57,647,723 XPMΒ·at block #6,800,457 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