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Home/Chain Registry/Block #1,120,791

Block #1,120,791

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2015, 9:40:19 AM Β· Difficulty 10.9362 Β· 5,706,177 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cc98b42a3bb0f4e1813a6bff1afb999affc4b521b3fa37ec40b189e8eef49f2b
View on Chainz β†—

Difficulty

10.936157

Transactions

2

Size

94.11 KB

Version

2

Bits

0aefa802

Nonce

634,218,164

Timestamp

6/21/2015, 9:40:19 AM

Confirmations

5,706,177

Merkle Root

8c6b61df83867eb8cae2a4aa5536d28e203f62787406ed6a4aa5422addd92260
Transactions (2)
Coinbased00704fe65c879…a2df6258968f8b
1 in β†’ 1 out9.3300 XPM110 B
Aby5KiwH…LZLo6kKR
1757606b74b8b9…ec6c19fda62312
649 in β†’ 2 out1500.0100 XPM93.91 KB
AYKArr5V…V9VqiqCZALgBMqKu…sXhd8qEo
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.

1.724 Γ— 10⁹⁢(97-digit number)
17246887317701956195…55387399394386144000
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
1.724 Γ— 10⁹⁢(97-digit number)
17246887317701956195…55387399394386143999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.724 Γ— 10⁹⁢(97-digit number)
17246887317701956195…55387399394386144001
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
3.449 Γ— 10⁹⁢(97-digit number)
34493774635403912390…10774798788772287999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.449 Γ— 10⁹⁢(97-digit number)
34493774635403912390…10774798788772288001
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
6.898 Γ— 10⁹⁢(97-digit number)
68987549270807824780…21549597577544575999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.898 Γ— 10⁹⁢(97-digit number)
68987549270807824780…21549597577544576001
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
1.379 Γ— 10⁹⁷(98-digit number)
13797509854161564956…43099195155089151999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.379 Γ— 10⁹⁷(98-digit number)
13797509854161564956…43099195155089152001
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
2.759 Γ— 10⁹⁷(98-digit number)
27595019708323129912…86198390310178303999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.759 Γ— 10⁹⁷(98-digit number)
27595019708323129912…86198390310178304001
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 1120791

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 cc98b42a3bb0f4e1813a6bff1afb999affc4b521b3fa37ec40b189e8eef49f2b

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 #1,120,791 on Chainz β†—
Circulating Supply:57,859,920 XPMΒ·at block #6,826,967 Β· updates every 60s
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