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Block #294,951

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/5/2013, 4:27:49 AM Β· Difficulty 9.9912 Β· 6,516,755 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f6c14080b5f072edf2c4bdd9ad561b5002798420d3f4dee33d9d0dc42aeb5cf9
View on Chainz β†—

Height

#294,951

Difficulty

9.991176

Transactions

1

Size

209 B

Version

2

Bits

09fdbdbd

Nonce

4,797

Timestamp

12/5/2013, 4:27:49 AM

Confirmations

6,516,755

Merkle Root

fce96b380db0b433e39e9db9aa83ef7882c0f638d41693f956d6a6ce2b63e87f
Transactions (1)
Coinbasefce96b380db0b4…d6a6ce2b63e87f
1 in β†’ 1 out10.0000 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.

4.809 Γ— 10¹⁰⁰(101-digit number)
48090619826204784142…81671148725731328000
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
4.809 Γ— 10¹⁰⁰(101-digit number)
48090619826204784142…81671148725731327999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.809 Γ— 10¹⁰⁰(101-digit number)
48090619826204784142…81671148725731328001
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
9.618 Γ— 10¹⁰⁰(101-digit number)
96181239652409568284…63342297451462655999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.618 Γ— 10¹⁰⁰(101-digit number)
96181239652409568284…63342297451462656001
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
1.923 Γ— 10¹⁰¹(102-digit number)
19236247930481913656…26684594902925311999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.923 Γ— 10¹⁰¹(102-digit number)
19236247930481913656…26684594902925312001
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
3.847 Γ— 10¹⁰¹(102-digit number)
38472495860963827313…53369189805850623999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.847 Γ— 10¹⁰¹(102-digit number)
38472495860963827313…53369189805850624001
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
7.694 Γ— 10¹⁰¹(102-digit number)
76944991721927654627…06738379611701247999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.694 Γ— 10¹⁰¹(102-digit number)
76944991721927654627…06738379611701248001
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 294951

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 f6c14080b5f072edf2c4bdd9ad561b5002798420d3f4dee33d9d0dc42aeb5cf9

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 #294,951 on Chainz β†—
Circulating Supply:57,737,759 XPMΒ·at block #6,811,705 Β· updates every 60s
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