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Home/Chain Registry/Block #1,408,661

Block #1,408,661

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2016, 11:30:10 AM Β· Difficulty 10.8051 Β· 5,431,452 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
199345636341ffafe570df466c18070d04a4d0ed2f4acf0fafb6b7bc67020420
View on Chainz β†—

Difficulty

10.805078

Transactions

2

Size

2.00 KB

Version

2

Bits

0ace1999

Nonce

776,890,417

Timestamp

1/11/2016, 11:30:10 AM

Confirmations

5,431,452

Merkle Root

0835c0eceed18e170fb974f77319c2615198e8b1a370f96db9247a644ea3c555
Transactions (2)
Coinbaseb6aac0b61bb9aa…cc33accc6f520d
1 in β†’ 1 out8.5700 XPM109 B
AbAhU74b…BwQgGuWi
a423c659ffaf02…9983412ecb5bc2
12 in β†’ 2 out223.9361 XPM1.81 KB
ARJUAwG8…5huRS93kATS8VF8N…kmv1UeYc
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.

7.767 Γ— 10⁹²(93-digit number)
77678432042002409701…83391217397160396800
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
7.767 Γ— 10⁹²(93-digit number)
77678432042002409701…83391217397160396799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.767 Γ— 10⁹²(93-digit number)
77678432042002409701…83391217397160396801
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
1.553 Γ— 10⁹³(94-digit number)
15535686408400481940…66782434794320793599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.553 Γ— 10⁹³(94-digit number)
15535686408400481940…66782434794320793601
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
3.107 Γ— 10⁹³(94-digit number)
31071372816800963880…33564869588641587199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.107 Γ— 10⁹³(94-digit number)
31071372816800963880…33564869588641587201
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
6.214 Γ— 10⁹³(94-digit number)
62142745633601927761…67129739177283174399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.214 Γ— 10⁹³(94-digit number)
62142745633601927761…67129739177283174401
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
1.242 Γ— 10⁹⁴(95-digit number)
12428549126720385552…34259478354566348799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.242 Γ— 10⁹⁴(95-digit number)
12428549126720385552…34259478354566348801
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 1408661

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 199345636341ffafe570df466c18070d04a4d0ed2f4acf0fafb6b7bc67020420

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 #1,408,661 on Chainz β†—
Circulating Supply:57,965,216 XPMΒ·at block #6,840,112 Β· updates every 60s
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