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Block #50,825

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 3:06:36 AM Β· Difficulty 8.8889 Β· 6,775,329 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
498ed7c53e1f2e20eeb3b3a2a85e2a596c6c3f38041cefdacd9f95bbb1282473
View on Chainz β†—

Height

#50,825

Difficulty

8.888885

Transactions

1

Size

201 B

Version

2

Bits

08e38df8

Nonce

571

Timestamp

7/16/2013, 3:06:36 AM

Confirmations

6,775,329

Merkle Root

b8009e66fde956c62ccabbd114aa9e7029fb9ad003a603aee0563ae561e1f0c0
Transactions (1)
Coinbaseb8009e66fde956…563ae561e1f0c0
1 in β†’ 1 out12.6400 XPM110 B
ARSnNA89…wjAP1LHZ
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.

2.164 Γ— 10⁹⁸(99-digit number)
21643271717307019625…36089418503877001920
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
2.164 Γ— 10⁹⁸(99-digit number)
21643271717307019625…36089418503877001919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.164 Γ— 10⁹⁸(99-digit number)
21643271717307019625…36089418503877001921
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
4.328 Γ— 10⁹⁸(99-digit number)
43286543434614039251…72178837007754003839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.328 Γ— 10⁹⁸(99-digit number)
43286543434614039251…72178837007754003841
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
8.657 Γ— 10⁹⁸(99-digit number)
86573086869228078502…44357674015508007679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.657 Γ— 10⁹⁸(99-digit number)
86573086869228078502…44357674015508007681
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
1.731 Γ— 10⁹⁹(100-digit number)
17314617373845615700…88715348031016015359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.731 Γ— 10⁹⁹(100-digit number)
17314617373845615700…88715348031016015361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 50825

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 498ed7c53e1f2e20eeb3b3a2a85e2a596c6c3f38041cefdacd9f95bbb1282473

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 #50,825 on Chainz β†—
Circulating Supply:57,853,358 XPMΒ·at block #6,826,153 Β· updates every 60s
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