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Block #271,146

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/24/2013, 11:01:58 AM Β· Difficulty 9.9516 Β· 6,555,083 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0afeefd676d9ee0424647517f3fa463b381b2f44089858f75eaf7ca337639123
View on Chainz β†—

Height

#271,146

Difficulty

9.951569

Transactions

1

Size

235 B

Version

2

Bits

09f39a08

Nonce

61,287

Timestamp

11/24/2013, 11:01:58 AM

Confirmations

6,555,083

Merkle Root

c9d47442d41597bbf14d2bc4cf845e73412904ddbdd885887b7d93f4fd36e00a
Transactions (1)
Coinbasec9d47442d41597…7d93f4fd36e00a
1 in β†’ 2 out10.0800 XPM141 B
AKcbk49N…GJbKa7j1AKNbfPoc…jfkpwAyL
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.

4.420 Γ— 10¹⁰⁴(105-digit number)
44209941226996181296…16926688451916208640
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
4.420 Γ— 10¹⁰⁴(105-digit number)
44209941226996181296…16926688451916208639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.420 Γ— 10¹⁰⁴(105-digit number)
44209941226996181296…16926688451916208641
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
8.841 Γ— 10¹⁰⁴(105-digit number)
88419882453992362593…33853376903832417279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.841 Γ— 10¹⁰⁴(105-digit number)
88419882453992362593…33853376903832417281
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
1.768 Γ— 10¹⁰⁡(106-digit number)
17683976490798472518…67706753807664834559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.768 Γ— 10¹⁰⁡(106-digit number)
17683976490798472518…67706753807664834561
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
3.536 Γ— 10¹⁰⁡(106-digit number)
35367952981596945037…35413507615329669119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.536 Γ— 10¹⁰⁡(106-digit number)
35367952981596945037…35413507615329669121
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
7.073 Γ— 10¹⁰⁡(106-digit number)
70735905963193890075…70827015230659338239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.073 Γ— 10¹⁰⁡(106-digit number)
70735905963193890075…70827015230659338241
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 271146

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 0afeefd676d9ee0424647517f3fa463b381b2f44089858f75eaf7ca337639123

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 #271,146 on Chainz β†—
Circulating Supply:57,853,966 XPMΒ·at block #6,826,228 Β· updates every 60s
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