XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,736,129

Block #1,736,129

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2016, 8:06:37 AM Β· Difficulty 10.7175 Β· 5,096,275 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
44f660f2c685f156c49db3f5affcdf556fb8d586a112835f4db85cb48f58fc02
View on Chainz β†—

Difficulty

10.717514

Transactions

2

Size

2.58 KB

Version

2

Bits

0ab7aefc

Nonce

848,895,769

Timestamp

8/27/2016, 8:06:37 AM

Confirmations

5,096,275

Merkle Root

57072cd74bada7ae0fd143f10d2c7c3cb4a51b80c21c8824ef833e3b5b7686b0
Transactions (2)
Coinbase496184b1536765…14d49f9fe6e56d
1 in β†’ 1 out8.7300 XPM110 B
AL4uLFMY…5MMEAriM
ffbf31cfc72b79…dbff1bcaccbc06
16 in β†’ 2 out4.9100 XPM2.39 KB
AWPvLEeT…xSmKE15zAGCdb3gj…7saDgdNm
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.

3.824 Γ— 10⁹⁡(96-digit number)
38245155360909220608…08109705574307810560
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
3.824 Γ— 10⁹⁡(96-digit number)
38245155360909220608…08109705574307810559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.824 Γ— 10⁹⁡(96-digit number)
38245155360909220608…08109705574307810561
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
7.649 Γ— 10⁹⁡(96-digit number)
76490310721818441217…16219411148615621119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.649 Γ— 10⁹⁡(96-digit number)
76490310721818441217…16219411148615621121
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
1.529 Γ— 10⁹⁢(97-digit number)
15298062144363688243…32438822297231242239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.529 Γ— 10⁹⁢(97-digit number)
15298062144363688243…32438822297231242241
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
3.059 Γ— 10⁹⁢(97-digit number)
30596124288727376486…64877644594462484479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.059 Γ— 10⁹⁢(97-digit number)
30596124288727376486…64877644594462484481
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
6.119 Γ— 10⁹⁢(97-digit number)
61192248577454752973…29755289188924968959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.119 Γ— 10⁹⁢(97-digit number)
61192248577454752973…29755289188924968961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1736129

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 44f660f2c685f156c49db3f5affcdf556fb8d586a112835f4db85cb48f58fc02

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 #1,736,129 on Chainz β†—
Circulating Supply:57,903,376 XPMΒ·at block #6,832,403 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy