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Block #262,831

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/17/2013, 6:01:13 AM Β· Difficulty 9.9676 Β· 6,537,694 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b283a82042916cbddf0c5615bff39d13306b77ee0e422fb4891ab5fcec1904fd
View on Chainz β†—

Height

#262,831

Difficulty

9.967597

Transactions

2

Size

1.72 KB

Version

2

Bits

09f7b474

Nonce

10,402

Timestamp

11/17/2013, 6:01:13 AM

Confirmations

6,537,694

Merkle Root

d2a975c3c0ca99438ccdaf34a230dfae0363c4a7b3c9a1b79d223bca9a7bf259
Transactions (2)
Coinbaseb3c76d868cb8c6…bb014f199a2f30
1 in β†’ 1 out10.0700 XPM109 B
AUuSo3HY…hnx3T5bc
b0d317d178e6b0…b69b98e0b35e30
10 in β†’ 2 out113.3099 XPM1.53 KB
AaZxZr7M…g3GFCpLUAYVhfyGv…1t3EWVG9
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.

7.578 Γ— 10⁹⁴(95-digit number)
75788985558229539241…25882625548917206600
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
7.578 Γ— 10⁹⁴(95-digit number)
75788985558229539241…25882625548917206599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.578 Γ— 10⁹⁴(95-digit number)
75788985558229539241…25882625548917206601
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
1.515 Γ— 10⁹⁡(96-digit number)
15157797111645907848…51765251097834413199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.515 Γ— 10⁹⁡(96-digit number)
15157797111645907848…51765251097834413201
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
3.031 Γ— 10⁹⁡(96-digit number)
30315594223291815696…03530502195668826399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.031 Γ— 10⁹⁡(96-digit number)
30315594223291815696…03530502195668826401
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
6.063 Γ— 10⁹⁡(96-digit number)
60631188446583631393…07061004391337652799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.063 Γ— 10⁹⁡(96-digit number)
60631188446583631393…07061004391337652801
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
1.212 Γ— 10⁹⁢(97-digit number)
12126237689316726278…14122008782675305599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.212 Γ— 10⁹⁢(97-digit number)
12126237689316726278…14122008782675305601
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 262831

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 b283a82042916cbddf0c5615bff39d13306b77ee0e422fb4891ab5fcec1904fd

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 #262,831 on Chainz β†—
Circulating Supply:57,648,267 XPMΒ·at block #6,800,524 Β· updates every 60s
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