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Block #452,082

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/20/2014, 9:02:38 AM Β· Difficulty 10.3829 Β· 6,363,048 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
350e2d5ec80574b60c626feb5367d790ef8d4316093ad5b4866735145f940e4f
View on Chainz β†—

Height

#452,082

Difficulty

10.382876

Transactions

1

Size

202 B

Version

2

Bits

0a620430

Nonce

82,167

Timestamp

3/20/2014, 9:02:38 AM

Confirmations

6,363,048

Merkle Root

f2121423a9106c44a2d22df4981e5373c3ed64511aa83398efe9e3a457baeac6
Transactions (1)
Coinbasef2121423a9106c…e9e3a457baeac6
1 in β†’ 1 out9.2600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.533 Γ— 10⁹⁹(100-digit number)
15336054817364208442…44448019384138240000
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
1.533 Γ— 10⁹⁹(100-digit number)
15336054817364208442…44448019384138239999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.533 Γ— 10⁹⁹(100-digit number)
15336054817364208442…44448019384138240001
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
3.067 Γ— 10⁹⁹(100-digit number)
30672109634728416884…88896038768276479999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.067 Γ— 10⁹⁹(100-digit number)
30672109634728416884…88896038768276480001
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
6.134 Γ— 10⁹⁹(100-digit number)
61344219269456833768…77792077536552959999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.134 Γ— 10⁹⁹(100-digit number)
61344219269456833768…77792077536552960001
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
1.226 Γ— 10¹⁰⁰(101-digit number)
12268843853891366753…55584155073105919999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.226 Γ— 10¹⁰⁰(101-digit number)
12268843853891366753…55584155073105920001
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
2.453 Γ— 10¹⁰⁰(101-digit number)
24537687707782733507…11168310146211839999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.453 Γ— 10¹⁰⁰(101-digit number)
24537687707782733507…11168310146211840001
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 452082

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 350e2d5ec80574b60c626feb5367d790ef8d4316093ad5b4866735145f940e4f

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 #452,082 on Chainz β†—
Circulating Supply:57,765,132 XPMΒ·at block #6,815,129 Β· updates every 60s
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