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Block #609,872

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/1/2014, 10:44:42 AM Β· Difficulty 10.9140 Β· 6,185,973 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5263c15f1643bf65dae92c9eea116d85fc3df677af0ea956d8f862df38af6cda
View on Chainz β†—

Height

#609,872

Difficulty

10.913994

Transactions

1

Size

208 B

Version

2

Bits

0ae9fb89

Nonce

11,989,287

Timestamp

7/1/2014, 10:44:42 AM

Confirmations

6,185,973

Merkle Root

6210d707757fa12e7f56fc123406c8240a974626a264c2bb24a2e08d3ade3c1e
Transactions (1)
Coinbase6210d707757fa1…a2e08d3ade3c1e
1 in β†’ 1 out8.3800 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.

4.148 Γ— 10⁹⁹(100-digit number)
41480022421876576057…70143289649108398080
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
4.148 Γ— 10⁹⁹(100-digit number)
41480022421876576057…70143289649108398079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.148 Γ— 10⁹⁹(100-digit number)
41480022421876576057…70143289649108398081
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
8.296 Γ— 10⁹⁹(100-digit number)
82960044843753152114…40286579298216796159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.296 Γ— 10⁹⁹(100-digit number)
82960044843753152114…40286579298216796161
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
1.659 Γ— 10¹⁰⁰(101-digit number)
16592008968750630422…80573158596433592319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.659 Γ— 10¹⁰⁰(101-digit number)
16592008968750630422…80573158596433592321
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
3.318 Γ— 10¹⁰⁰(101-digit number)
33184017937501260845…61146317192867184639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.318 Γ— 10¹⁰⁰(101-digit number)
33184017937501260845…61146317192867184641
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
6.636 Γ— 10¹⁰⁰(101-digit number)
66368035875002521691…22292634385734369279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.636 Γ— 10¹⁰⁰(101-digit number)
66368035875002521691…22292634385734369281
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 609872

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 5263c15f1643bf65dae92c9eea116d85fc3df677af0ea956d8f862df38af6cda

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 #609,872 on Chainz β†—
Circulating Supply:57,610,844 XPMΒ·at block #6,795,844 Β· updates every 60s
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