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Home/Chain Registry/Block #2,099,732

Block #2,099,732

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/4/2017, 4:53:28 PM Β· Difficulty 10.8562 Β· 4,743,912 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f580f4a6ac4a8eab3633479ba3c1bd0b9a834d4b515dba7925d6eaf1a220794a
View on Chainz β†—

Difficulty

10.856214

Transactions

1

Size

199 B

Version

2

Bits

0adb30d7

Nonce

1,949,537,090

Timestamp

5/4/2017, 4:53:28 PM

Confirmations

4,743,912

Merkle Root

d60463dbff021f9fc9a9d58a15356d9aaaaa827f1600e2a853eb74f2fdcfcf00
Transactions (1)
Coinbased60463dbff021f…eb74f2fdcfcf00
1 in β†’ 1 out8.4700 XPM109 B
ARdzXH7F…Yd3NYj3t
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.

1.322 Γ— 10⁹⁡(96-digit number)
13221009563124534077…39034619878052871040
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
1.322 Γ— 10⁹⁡(96-digit number)
13221009563124534077…39034619878052871039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.322 Γ— 10⁹⁡(96-digit number)
13221009563124534077…39034619878052871041
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
2.644 Γ— 10⁹⁡(96-digit number)
26442019126249068154…78069239756105742079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.644 Γ— 10⁹⁡(96-digit number)
26442019126249068154…78069239756105742081
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
5.288 Γ— 10⁹⁡(96-digit number)
52884038252498136309…56138479512211484159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.288 Γ— 10⁹⁡(96-digit number)
52884038252498136309…56138479512211484161
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
1.057 Γ— 10⁹⁢(97-digit number)
10576807650499627261…12276959024422968319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.057 Γ— 10⁹⁢(97-digit number)
10576807650499627261…12276959024422968321
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
2.115 Γ— 10⁹⁢(97-digit number)
21153615300999254523…24553918048845936639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.115 Γ— 10⁹⁢(97-digit number)
21153615300999254523…24553918048845936641
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
4.230 Γ— 10⁹⁢(97-digit number)
42307230601998509047…49107836097691873279
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 2099732

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 f580f4a6ac4a8eab3633479ba3c1bd0b9a834d4b515dba7925d6eaf1a220794a

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 #2,099,732 on Chainz β†—
Circulating Supply:57,993,522 XPMΒ·at block #6,843,643 Β· updates every 60s
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