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Block #529,590

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/7/2014, 8:31:54 AM Β· Difficulty 10.8902 Β· 6,312,564 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ae2ee71dfd2eeb3f29626abbb45ea1a2cb02681e275b7fa8b758d5fb8b51df49
View on Chainz β†—

Height

#529,590

Difficulty

10.890153

Transactions

2

Size

582 B

Version

2

Bits

0ae3e111

Nonce

24,730,678

Timestamp

5/7/2014, 8:31:54 AM

Confirmations

6,312,564

Merkle Root

b8236d03eaa96b38f07fd5fc72cc757fe60662ec7a2c26ea88c38e7fc1fcb835
Transactions (2)
Coinbase7080be1025aa69…83ef31904aef53
1 in β†’ 1 out8.4400 XPM116 B
ANSXnLY2…Sd25TjkD
cbf702f16dd958…9a563110f639d3
2 in β†’ 2 out49.1900 XPM375 B
AcBvLaSu…X3gaHvJ1AXc7mrpx…BeBASVUJ
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.

1.568 Γ— 10⁹⁸(99-digit number)
15688058892994209271…47562083481498434400
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
1.568 Γ— 10⁹⁸(99-digit number)
15688058892994209271…47562083481498434399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.568 Γ— 10⁹⁸(99-digit number)
15688058892994209271…47562083481498434401
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
3.137 Γ— 10⁹⁸(99-digit number)
31376117785988418542…95124166962996868799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.137 Γ— 10⁹⁸(99-digit number)
31376117785988418542…95124166962996868801
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
6.275 Γ— 10⁹⁸(99-digit number)
62752235571976837084…90248333925993737599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.275 Γ— 10⁹⁸(99-digit number)
62752235571976837084…90248333925993737601
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
1.255 Γ— 10⁹⁹(100-digit number)
12550447114395367416…80496667851987475199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.255 Γ— 10⁹⁹(100-digit number)
12550447114395367416…80496667851987475201
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
2.510 Γ— 10⁹⁹(100-digit number)
25100894228790734833…60993335703974950399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.510 Γ— 10⁹⁹(100-digit number)
25100894228790734833…60993335703974950401
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 529590

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 ae2ee71dfd2eeb3f29626abbb45ea1a2cb02681e275b7fa8b758d5fb8b51df49

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 #529,590 on Chainz β†—
Circulating Supply:57,981,622 XPMΒ·at block #6,842,153 Β· updates every 60s
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