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Block #504,931

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/22/2014, 2:49:34 AM Β· Difficulty 10.8099 Β· 6,321,570 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eb8170145a3697a362b92a837433ba2068e208636b121ea7e4d1fc6c1f5ec458
View on Chainz β†—

Height

#504,931

Difficulty

10.809894

Transactions

2

Size

430 B

Version

2

Bits

0acf5538

Nonce

364,651,615

Timestamp

4/22/2014, 2:49:34 AM

Confirmations

6,321,570

Merkle Root

372a4e374f4209d3201ee63febfea265e2efe71314904581137b16ab76308316
Transactions (2)
Coinbased8beb9249e1064…df5cf8b3df121e
1 in β†’ 1 out8.5500 XPM111 B
AQN9zjjL…uLg3c11a
61d6f7d1cd2047…c658fb0741f213
1 in β†’ 2 out1.8132 XPM227 B
AUPdsbk8…sWDAh678AXu8B3yL…5g33w9LG
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.

2.322 Γ— 10⁹⁹(100-digit number)
23224650719678690525…03240433392162195200
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
2.322 Γ— 10⁹⁹(100-digit number)
23224650719678690525…03240433392162195199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.322 Γ— 10⁹⁹(100-digit number)
23224650719678690525…03240433392162195201
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
4.644 Γ— 10⁹⁹(100-digit number)
46449301439357381051…06480866784324390399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.644 Γ— 10⁹⁹(100-digit number)
46449301439357381051…06480866784324390401
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
9.289 Γ— 10⁹⁹(100-digit number)
92898602878714762103…12961733568648780799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.289 Γ— 10⁹⁹(100-digit number)
92898602878714762103…12961733568648780801
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
1.857 Γ— 10¹⁰⁰(101-digit number)
18579720575742952420…25923467137297561599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.857 Γ— 10¹⁰⁰(101-digit number)
18579720575742952420…25923467137297561601
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
3.715 Γ— 10¹⁰⁰(101-digit number)
37159441151485904841…51846934274595123199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.715 Γ— 10¹⁰⁰(101-digit number)
37159441151485904841…51846934274595123201
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
7.431 Γ— 10¹⁰⁰(101-digit number)
74318882302971809682…03693868549190246399
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 504931

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 eb8170145a3697a362b92a837433ba2068e208636b121ea7e4d1fc6c1f5ec458

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 #504,931 on Chainz β†—
Circulating Supply:57,856,150 XPMΒ·at block #6,826,500 Β· updates every 60s
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