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Home/Chain Registry/Block #1,736,130

Block #1,736,130

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2016, 8:07:07 AM Β· Difficulty 10.7173 Β· 5,095,746 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
863bf2a656f495f16f350daf44d2728965dc23b152c778698b22ec3c38aa963c
View on Chainz β†—

Difficulty

10.717331

Transactions

1

Size

199 B

Version

2

Bits

0ab7a2fd

Nonce

574,760,377

Timestamp

8/27/2016, 8:07:07 AM

Confirmations

5,095,746

Merkle Root

e21a56c01db0d3f5f7c9b5c401efc30fc0520598f506f228f908a1ee12e40ff4
Transactions (1)
Coinbasee21a56c01db0d3…08a1ee12e40ff4
1 in β†’ 1 out8.6900 XPM109 B
AaviNJWE…FvmkpLLr
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.

4.564 Γ— 10⁹⁴(95-digit number)
45642305725555927149…63231755898188212960
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
4.564 Γ— 10⁹⁴(95-digit number)
45642305725555927149…63231755898188212959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.564 Γ— 10⁹⁴(95-digit number)
45642305725555927149…63231755898188212961
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
9.128 Γ— 10⁹⁴(95-digit number)
91284611451111854298…26463511796376425919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.128 Γ— 10⁹⁴(95-digit number)
91284611451111854298…26463511796376425921
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
1.825 Γ— 10⁹⁡(96-digit number)
18256922290222370859…52927023592752851839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.825 Γ— 10⁹⁡(96-digit number)
18256922290222370859…52927023592752851841
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
3.651 Γ— 10⁹⁡(96-digit number)
36513844580444741719…05854047185505703679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.651 Γ— 10⁹⁡(96-digit number)
36513844580444741719…05854047185505703681
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
7.302 Γ— 10⁹⁡(96-digit number)
73027689160889483438…11708094371011407359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.302 Γ— 10⁹⁡(96-digit number)
73027689160889483438…11708094371011407361
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 1736130

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 863bf2a656f495f16f350daf44d2728965dc23b152c778698b22ec3c38aa963c

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 #1,736,130 on Chainz β†—
Circulating Supply:57,899,131 XPMΒ·at block #6,831,875 Β· updates every 60s
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