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Home/Chain Registry/Block #2,825,504

Block #2,825,504

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2018, 7:27:57 AM Β· Difficulty 11.7097 Β· 4,019,782 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9a34b8c3c278fc15729f7fd4c29496aeefe8839ec526cd10ebbc4ad10fa5842a
View on Chainz β†—

Difficulty

11.709739

Transactions

1

Size

201 B

Version

2

Bits

0bb5b176

Nonce

1,318,928,190

Timestamp

9/5/2018, 7:27:57 AM

Confirmations

4,019,782

Merkle Root

5f8bf1f9eb21284849e30ecfbb183d3669ccdace50b5324d47635587c80417ea
Transactions (1)
Coinbase5f8bf1f9eb2128…635587c80417ea
1 in β†’ 1 out7.2800 XPM110 B
APkX8DHf…C4AY6s7Z
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.

3.620 Γ— 10⁹⁷(98-digit number)
36207495035444864952…28529460737665054720
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
3.620 Γ— 10⁹⁷(98-digit number)
36207495035444864952…28529460737665054719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.620 Γ— 10⁹⁷(98-digit number)
36207495035444864952…28529460737665054721
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
7.241 Γ— 10⁹⁷(98-digit number)
72414990070889729904…57058921475330109439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.241 Γ— 10⁹⁷(98-digit number)
72414990070889729904…57058921475330109441
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
1.448 Γ— 10⁹⁸(99-digit number)
14482998014177945980…14117842950660218879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.448 Γ— 10⁹⁸(99-digit number)
14482998014177945980…14117842950660218881
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
2.896 Γ— 10⁹⁸(99-digit number)
28965996028355891961…28235685901320437759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.896 Γ— 10⁹⁸(99-digit number)
28965996028355891961…28235685901320437761
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
5.793 Γ— 10⁹⁸(99-digit number)
57931992056711783923…56471371802640875519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.793 Γ— 10⁹⁸(99-digit number)
57931992056711783923…56471371802640875521
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
1.158 Γ— 10⁹⁹(100-digit number)
11586398411342356784…12942743605281751039
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 2825504

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 9a34b8c3c278fc15729f7fd4c29496aeefe8839ec526cd10ebbc4ad10fa5842a

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 #2,825,504 on Chainz β†—
Circulating Supply:58,006,725 XPMΒ·at block #6,845,285 Β· updates every 60s
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