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Block #540,323

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/13/2014, 2:08:52 AM Β· Difficulty 10.9331 Β· 6,256,067 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9360589b77bc363c7ffa1e0665a66566e4a4bca3cfa26ff84ed0b4a02d1dfd11
View on Chainz β†—

Height

#540,323

Difficulty

10.933093

Transactions

1

Size

208 B

Version

2

Bits

0aeedf2b

Nonce

12,979,944

Timestamp

5/13/2014, 2:08:52 AM

Confirmations

6,256,067

Merkle Root

20011c446a47091b276ced1824fbf04b3151a16fb2c2a8f8dad2d6fccef5f0f3
Transactions (1)
Coinbase20011c446a4709…d2d6fccef5f0f3
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.904 Γ— 10⁹⁸(99-digit number)
39045902475056347000…44667341762383912960
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
3.904 Γ— 10⁹⁸(99-digit number)
39045902475056347000…44667341762383912959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.904 Γ— 10⁹⁸(99-digit number)
39045902475056347000…44667341762383912961
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
7.809 Γ— 10⁹⁸(99-digit number)
78091804950112694000…89334683524767825919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.809 Γ— 10⁹⁸(99-digit number)
78091804950112694000…89334683524767825921
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
1.561 Γ— 10⁹⁹(100-digit number)
15618360990022538800…78669367049535651839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.561 Γ— 10⁹⁹(100-digit number)
15618360990022538800…78669367049535651841
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
3.123 Γ— 10⁹⁹(100-digit number)
31236721980045077600…57338734099071303679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.123 Γ— 10⁹⁹(100-digit number)
31236721980045077600…57338734099071303681
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
6.247 Γ— 10⁹⁹(100-digit number)
62473443960090155200…14677468198142607359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.247 Γ— 10⁹⁹(100-digit number)
62473443960090155200…14677468198142607361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.249 Γ— 10¹⁰⁰(101-digit number)
12494688792018031040…29354936396285214719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 540323

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 9360589b77bc363c7ffa1e0665a66566e4a4bca3cfa26ff84ed0b4a02d1dfd11

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 #540,323 on Chainz β†—
Circulating Supply:57,615,116 XPMΒ·at block #6,796,389 Β· updates every 60s
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