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Home/Chain Registry/Block #2,285,133

Block #2,285,133

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2017, 4:08:53 PM Β· Difficulty 10.9553 Β· 4,548,207 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f9955d9ce3f50d8648dab3221c761f8128fc1cf34ddc5d52795049f1143a75d4
View on Chainz β†—

Difficulty

10.955335

Transactions

2

Size

426 B

Version

2

Bits

0af490d3

Nonce

139,521,663

Timestamp

9/6/2017, 4:08:53 PM

Confirmations

4,548,207

Merkle Root

d621235135de4ec6cbf9e5fce82557cbbc91b20270c79acee820b574ad9c20d0
Transactions (2)
Coinbase0d54985fa22e9e…e0d593f6e4f92d
1 in β†’ 1 out8.3300 XPM110 B
AKaqsSCw…4a8LPq6V
e5744744dfd84b…1d3b27cc9d33cd
1 in β†’ 2 out1484.6602 XPM226 B
AS8Swa5k…emSJQqiEAa12fnFH…hVG6PKXV
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.

4.792 Γ— 10⁹⁡(96-digit number)
47928849855397499257…35928323733984335360
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
4.792 Γ— 10⁹⁡(96-digit number)
47928849855397499257…35928323733984335359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.792 Γ— 10⁹⁡(96-digit number)
47928849855397499257…35928323733984335361
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
9.585 Γ— 10⁹⁡(96-digit number)
95857699710794998514…71856647467968670719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.585 Γ— 10⁹⁡(96-digit number)
95857699710794998514…71856647467968670721
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
1.917 Γ— 10⁹⁢(97-digit number)
19171539942158999702…43713294935937341439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.917 Γ— 10⁹⁢(97-digit number)
19171539942158999702…43713294935937341441
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
3.834 Γ— 10⁹⁢(97-digit number)
38343079884317999405…87426589871874682879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.834 Γ— 10⁹⁢(97-digit number)
38343079884317999405…87426589871874682881
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
7.668 Γ— 10⁹⁢(97-digit number)
76686159768635998811…74853179743749365759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.668 Γ— 10⁹⁢(97-digit number)
76686159768635998811…74853179743749365761
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 2285133

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 f9955d9ce3f50d8648dab3221c761f8128fc1cf34ddc5d52795049f1143a75d4

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 #2,285,133 on Chainz β†—
Circulating Supply:57,910,915 XPMΒ·at block #6,833,339 Β· updates every 60s
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