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Home/Chain Registry/Block #2,836,998

Block #2,836,998

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2018, 5:03:04 AM Β· Difficulty 11.7170 Β· 4,005,889 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bf51c813a8094c2adeb23a46f220ce1eafee436b7ee5c351e0222af95026aa69
View on Chainz β†—

Difficulty

11.717034

Transactions

1

Size

201 B

Version

2

Bits

0bb78f88

Nonce

1,695,571,534

Timestamp

9/13/2018, 5:03:04 AM

Confirmations

4,005,889

Merkle Root

6f6465eead7c550df85296b15117e1207af45f4abd5bede448d1034a4e4aad3b
Transactions (1)
Coinbase6f6465eead7c55…d1034a4e4aad3b
1 in β†’ 1 out7.2700 XPM110 B
ARSFtJQJ…ZANVUTTN
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.

1.155 Γ— 10⁹⁸(99-digit number)
11556980918933110444…29141600859559034880
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
1.155 Γ— 10⁹⁸(99-digit number)
11556980918933110444…29141600859559034879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.155 Γ— 10⁹⁸(99-digit number)
11556980918933110444…29141600859559034881
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
2.311 Γ— 10⁹⁸(99-digit number)
23113961837866220889…58283201719118069759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.311 Γ— 10⁹⁸(99-digit number)
23113961837866220889…58283201719118069761
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
4.622 Γ— 10⁹⁸(99-digit number)
46227923675732441779…16566403438236139519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.622 Γ— 10⁹⁸(99-digit number)
46227923675732441779…16566403438236139521
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
9.245 Γ— 10⁹⁸(99-digit number)
92455847351464883558…33132806876472279039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.245 Γ— 10⁹⁸(99-digit number)
92455847351464883558…33132806876472279041
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
1.849 Γ— 10⁹⁹(100-digit number)
18491169470292976711…66265613752944558079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.849 Γ— 10⁹⁹(100-digit number)
18491169470292976711…66265613752944558081
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
3.698 Γ— 10⁹⁹(100-digit number)
36982338940585953423…32531227505889116159
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 2836998

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 bf51c813a8094c2adeb23a46f220ce1eafee436b7ee5c351e0222af95026aa69

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 #2,836,998 on Chainz β†—
Circulating Supply:57,987,442 XPMΒ·at block #6,842,886 Β· updates every 60s
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