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Block #536,260

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/11/2014, 8:25:28 AM Β· Difficulty 10.9087 Β· 6,309,125 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
58c0f48f4b9d1ef227c278a5e4f5fd732f65cde9239c5e64d60c7d30bf3d9cf1
View on Chainz β†—

Height

#536,260

Difficulty

10.908667

Transactions

1

Size

209 B

Version

2

Bits

0ae89e67

Nonce

100,170,296

Timestamp

5/11/2014, 8:25:28 AM

Confirmations

6,309,125

Merkle Root

0cd41276fb47757584dac196659cf810073890cf82e0430da2b4412713288b81
Transactions (1)
Coinbase0cd41276fb4775…b4412713288b81
1 in β†’ 1 out8.3900 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.

8.499 Γ— 10¹⁰⁰(101-digit number)
84997277265797878224…23305209443102064640
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
8.499 Γ— 10¹⁰⁰(101-digit number)
84997277265797878224…23305209443102064639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.499 Γ— 10¹⁰⁰(101-digit number)
84997277265797878224…23305209443102064641
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
1.699 Γ— 10¹⁰¹(102-digit number)
16999455453159575644…46610418886204129279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.699 Γ— 10¹⁰¹(102-digit number)
16999455453159575644…46610418886204129281
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
3.399 Γ— 10¹⁰¹(102-digit number)
33998910906319151289…93220837772408258559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.399 Γ— 10¹⁰¹(102-digit number)
33998910906319151289…93220837772408258561
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
6.799 Γ— 10¹⁰¹(102-digit number)
67997821812638302579…86441675544816517119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.799 Γ— 10¹⁰¹(102-digit number)
67997821812638302579…86441675544816517121
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
1.359 Γ— 10¹⁰²(103-digit number)
13599564362527660515…72883351089633034239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.359 Γ— 10¹⁰²(103-digit number)
13599564362527660515…72883351089633034241
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 536260

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 58c0f48f4b9d1ef227c278a5e4f5fd732f65cde9239c5e64d60c7d30bf3d9cf1

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 #536,260 on Chainz β†—
Circulating Supply:58,007,524 XPMΒ·at block #6,845,384 Β· updates every 60s
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