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Block #852,013

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2014, 6:20:37 PM Β· Difficulty 10.9702 Β· 5,974,441 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7f9c6d3e89927ae3aa430cf477a2c3ab28212a22b8689eb49aba36b8090ed025
View on Chainz β†—

Height

#852,013

Difficulty

10.970161

Transactions

2

Size

574 B

Version

2

Bits

0af85c7f

Nonce

346,551,907

Timestamp

12/13/2014, 6:20:37 PM

Confirmations

5,974,441

Merkle Root

c6a7ae08d8756c704389af346179baee943867469cab2878ef1ba3305aac730f
Transactions (2)
Coinbased17ca27a6c7afb…94c0b9dac729e7
1 in β†’ 1 out8.3100 XPM110 B
AbdE6yug…pdKFk6aw
590cb9dc5e69f2…d3f6f9f7def73b
2 in β†’ 2 out14.4982 XPM374 B
AT6hERnY…5615mjajAUY54LT9…Q8pWMHVG
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.

7.152 Γ— 10⁹⁴(95-digit number)
71527224518555881932…37993210026888668960
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
7.152 Γ— 10⁹⁴(95-digit number)
71527224518555881932…37993210026888668959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.152 Γ— 10⁹⁴(95-digit number)
71527224518555881932…37993210026888668961
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
1.430 Γ— 10⁹⁡(96-digit number)
14305444903711176386…75986420053777337919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.430 Γ— 10⁹⁡(96-digit number)
14305444903711176386…75986420053777337921
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
2.861 Γ— 10⁹⁡(96-digit number)
28610889807422352772…51972840107554675839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.861 Γ— 10⁹⁡(96-digit number)
28610889807422352772…51972840107554675841
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
5.722 Γ— 10⁹⁡(96-digit number)
57221779614844705545…03945680215109351679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.722 Γ— 10⁹⁡(96-digit number)
57221779614844705545…03945680215109351681
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
1.144 Γ— 10⁹⁢(97-digit number)
11444355922968941109…07891360430218703359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.144 Γ— 10⁹⁢(97-digit number)
11444355922968941109…07891360430218703361
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 852013

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 7f9c6d3e89927ae3aa430cf477a2c3ab28212a22b8689eb49aba36b8090ed025

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 #852,013 on Chainz β†—
Circulating Supply:57,855,769 XPMΒ·at block #6,826,453 Β· updates every 60s
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