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Home/Chain Registry/Block #2,649,479

Block #2,649,479

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2018, 6:54:21 AM Β· Difficulty 11.7637 Β· 4,183,520 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0f5c31839b9a6ca844e95f50637085b648bb57e898527fc540caba8d9ef93459
View on Chainz β†—

Difficulty

11.763678

Transactions

1

Size

199 B

Version

2

Bits

0bc38063

Nonce

542,473,248

Timestamp

5/5/2018, 6:54:21 AM

Confirmations

4,183,520

Merkle Root

cca6d69281d93a9672b6d0b2abbf886f81801487ec0746411c14308fb9a7bcd3
Transactions (1)
Coinbasecca6d69281d93a…14308fb9a7bcd3
1 in β†’ 1 out7.2100 XPM109 B
Adqah8zh…1WwoHJ9t
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.

4.870 Γ— 10⁹⁡(96-digit number)
48707801309000158853…55104901913356379200
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
4.870 Γ— 10⁹⁡(96-digit number)
48707801309000158853…55104901913356379199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.870 Γ— 10⁹⁡(96-digit number)
48707801309000158853…55104901913356379201
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
9.741 Γ— 10⁹⁡(96-digit number)
97415602618000317706…10209803826712758399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.741 Γ— 10⁹⁡(96-digit number)
97415602618000317706…10209803826712758401
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
1.948 Γ— 10⁹⁢(97-digit number)
19483120523600063541…20419607653425516799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.948 Γ— 10⁹⁢(97-digit number)
19483120523600063541…20419607653425516801
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
3.896 Γ— 10⁹⁢(97-digit number)
38966241047200127082…40839215306851033599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.896 Γ— 10⁹⁢(97-digit number)
38966241047200127082…40839215306851033601
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
7.793 Γ— 10⁹⁢(97-digit number)
77932482094400254165…81678430613702067199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.793 Γ— 10⁹⁢(97-digit number)
77932482094400254165…81678430613702067201
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
1.558 Γ— 10⁹⁷(98-digit number)
15586496418880050833…63356861227404134399
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 2649479

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 0f5c31839b9a6ca844e95f50637085b648bb57e898527fc540caba8d9ef93459

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 #2,649,479 on Chainz β†—
Circulating Supply:57,908,165 XPMΒ·at block #6,832,998 Β· updates every 60s
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