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Block #225,408

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/24/2013, 11:17:10 AM Β· Difficulty 9.9367 Β· 6,578,597 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c26862977baf4bb130a89be46c4a7654c60dc48ae3a1623023480d7449b4a19f
View on Chainz β†—

Height

#225,408

Difficulty

9.936748

Transactions

1

Size

209 B

Version

2

Bits

09efcebe

Nonce

31,259

Timestamp

10/24/2013, 11:17:10 AM

Confirmations

6,578,597

Merkle Root

56c27347c6574ffff23115edd39d09e19e16a0934bc1ba251fcf66f1a1c5cae7
Transactions (1)
Coinbase56c27347c6574f…cf66f1a1c5cae7
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

7.416 Γ— 10¹⁰⁰(101-digit number)
74162367568499244762…98914846926508267520
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
7.416 Γ— 10¹⁰⁰(101-digit number)
74162367568499244762…98914846926508267519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.416 Γ— 10¹⁰⁰(101-digit number)
74162367568499244762…98914846926508267521
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
1.483 Γ— 10¹⁰¹(102-digit number)
14832473513699848952…97829693853016535039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.483 Γ— 10¹⁰¹(102-digit number)
14832473513699848952…97829693853016535041
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
2.966 Γ— 10¹⁰¹(102-digit number)
29664947027399697905…95659387706033070079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.966 Γ— 10¹⁰¹(102-digit number)
29664947027399697905…95659387706033070081
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
5.932 Γ— 10¹⁰¹(102-digit number)
59329894054799395810…91318775412066140159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.932 Γ— 10¹⁰¹(102-digit number)
59329894054799395810…91318775412066140161
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
1.186 Γ— 10¹⁰²(103-digit number)
11865978810959879162…82637550824132280319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.186 Γ— 10¹⁰²(103-digit number)
11865978810959879162…82637550824132280321
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 225408

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 c26862977baf4bb130a89be46c4a7654c60dc48ae3a1623023480d7449b4a19f

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 #225,408 on Chainz β†—
Circulating Supply:57,676,087 XPMΒ·at block #6,804,004 Β· updates every 60s
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