XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #229,226

Block #229,226

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/27/2013, 1:19:55 AM Β· Difficulty 9.9381 Β· 6,565,180 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
139a56bc47014a847b855ed573afd1169ea1f0baa7a5a14f5e50523c4340bdec
View on Chainz β†—

Height

#229,226

Difficulty

9.938065

Transactions

1

Size

210 B

Version

2

Bits

09f02504

Nonce

50,513,098

Timestamp

10/27/2013, 1:19:55 AM

Confirmations

6,565,180

Merkle Root

2dd094c6a1259654327be982abeb1d330b22ec0e3e309f6e2ab65d4348392160
Transactions (1)
Coinbase2dd094c6a12596…b65d4348392160
1 in β†’ 1 out10.1100 XPM118 B
AUMdiAvZ…5asatyd4
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.

1.978 Γ— 10⁹⁹(100-digit number)
19784779499646674900…91859758189358323200
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
1.978 Γ— 10⁹⁹(100-digit number)
19784779499646674900…91859758189358323199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.978 Γ— 10⁹⁹(100-digit number)
19784779499646674900…91859758189358323201
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
3.956 Γ— 10⁹⁹(100-digit number)
39569558999293349800…83719516378716646399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.956 Γ— 10⁹⁹(100-digit number)
39569558999293349800…83719516378716646401
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
7.913 Γ— 10⁹⁹(100-digit number)
79139117998586699601…67439032757433292799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.913 Γ— 10⁹⁹(100-digit number)
79139117998586699601…67439032757433292801
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
1.582 Γ— 10¹⁰⁰(101-digit number)
15827823599717339920…34878065514866585599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.582 Γ— 10¹⁰⁰(101-digit number)
15827823599717339920…34878065514866585601
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
3.165 Γ— 10¹⁰⁰(101-digit number)
31655647199434679840…69756131029733171199
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 229226

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 139a56bc47014a847b855ed573afd1169ea1f0baa7a5a14f5e50523c4340bdec

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 #229,226 on Chainz β†—
Circulating Supply:57,599,280 XPMΒ·at block #6,794,405 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