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Home/Chain Registry/Block #2,649,924

Block #2,649,924

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2018, 3:25:09 PM Β· Difficulty 11.7606 Β· 4,186,847 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
49a344086075a0d5c4ac4c7b92d4ed1d9b924a7b20c4735ea383e74de76052e7
View on Chainz β†—

Difficulty

11.760599

Transactions

2

Size

723 B

Version

2

Bits

0bc2b69d

Nonce

1,918,034,011

Timestamp

5/5/2018, 3:25:09 PM

Confirmations

4,186,847

Merkle Root

5064f608ee8923577f71875a5fdf1dc1e5a3aae0325de95b4c5852dea1316148
Transactions (2)
Coinbase5346556a2bdd7f…8916aa991bdfcc
1 in β†’ 1 out7.2300 XPM110 B
Adqah8zh…1WwoHJ9t
725d931bcdfcc6…31398199550877
3 in β†’ 2 out73.0089 XPM523 B
AFpHJhDK…hyA1PvSQAc4q35ij…6o21NWaM
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.

1.137 Γ— 10⁹⁴(95-digit number)
11376357395468334451…70380854407835155720
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
1.137 Γ— 10⁹⁴(95-digit number)
11376357395468334451…70380854407835155719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.137 Γ— 10⁹⁴(95-digit number)
11376357395468334451…70380854407835155721
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
2.275 Γ— 10⁹⁴(95-digit number)
22752714790936668903…40761708815670311439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.275 Γ— 10⁹⁴(95-digit number)
22752714790936668903…40761708815670311441
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
4.550 Γ— 10⁹⁴(95-digit number)
45505429581873337806…81523417631340622879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.550 Γ— 10⁹⁴(95-digit number)
45505429581873337806…81523417631340622881
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
9.101 Γ— 10⁹⁴(95-digit number)
91010859163746675613…63046835262681245759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.101 Γ— 10⁹⁴(95-digit number)
91010859163746675613…63046835262681245761
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
1.820 Γ— 10⁹⁡(96-digit number)
18202171832749335122…26093670525362491519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.820 Γ— 10⁹⁡(96-digit number)
18202171832749335122…26093670525362491521
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
3.640 Γ— 10⁹⁡(96-digit number)
36404343665498670245…52187341050724983039
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 2649924

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 49a344086075a0d5c4ac4c7b92d4ed1d9b924a7b20c4735ea383e74de76052e7

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 #2,649,924 on Chainz β†—
Circulating Supply:57,938,445 XPMΒ·at block #6,836,770 Β· updates every 60s
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