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Home/Chain Registry/Block #1,446,543

Block #1,446,543

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/7/2016, 1:03:58 PM Β· Difficulty 10.7593 Β· 5,380,543 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e43ffddd0d83d59c37877f2fa354a5f9d4b84b1173777a083cfd80ec899cba38
View on Chainz β†—

Difficulty

10.759330

Transactions

1

Size

243 B

Version

2

Bits

0ac2637b

Nonce

179,632,260

Timestamp

2/7/2016, 1:03:58 PM

Confirmations

5,380,543

Merkle Root

dfb9970a23e566fda50dc1772f540480a793f6608da2c2d2284b757c4dbf239e
Transactions (1)
Coinbasedfb9970a23e566…4b757c4dbf239e
1 in β†’ 2 out8.6200 XPM152 B
AXyURe5W…4RkBkCpGALPu3s2c…EJXLjVFh
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.

1.312 Γ— 10⁹⁸(99-digit number)
13122487831486060759…08096750796196858880
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
1.312 Γ— 10⁹⁸(99-digit number)
13122487831486060759…08096750796196858879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.312 Γ— 10⁹⁸(99-digit number)
13122487831486060759…08096750796196858881
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
2.624 Γ— 10⁹⁸(99-digit number)
26244975662972121518…16193501592393717759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.624 Γ— 10⁹⁸(99-digit number)
26244975662972121518…16193501592393717761
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
5.248 Γ— 10⁹⁸(99-digit number)
52489951325944243036…32387003184787435519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.248 Γ— 10⁹⁸(99-digit number)
52489951325944243036…32387003184787435521
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
1.049 Γ— 10⁹⁹(100-digit number)
10497990265188848607…64774006369574871039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.049 Γ— 10⁹⁹(100-digit number)
10497990265188848607…64774006369574871041
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
2.099 Γ— 10⁹⁹(100-digit number)
20995980530377697214…29548012739149742079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.099 Γ— 10⁹⁹(100-digit number)
20995980530377697214…29548012739149742081
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 1446543

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 e43ffddd0d83d59c37877f2fa354a5f9d4b84b1173777a083cfd80ec899cba38

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 #1,446,543 on Chainz β†—
Circulating Supply:57,860,873 XPMΒ·at block #6,827,085 Β· updates every 60s
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