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Block #840,774

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/5/2014, 9:38:30 AM Β· Difficulty 10.9742 Β· 6,004,582 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2dcea2d67468fb44a437da60a8d9a83c16a32596f33259c119e8baff0aa7f62a
View on Chainz β†—

Height

#840,774

Difficulty

10.974232

Transactions

2

Size

698 B

Version

2

Bits

0af9673f

Nonce

411,563,775

Timestamp

12/5/2014, 9:38:30 AM

Confirmations

6,004,582

Merkle Root

7ec02ce48e16e7398da1acfc5f355f916e15faa9724081f7fe77251361d849ac
Transactions (2)
Coinbase0352e54eea206f…cbe8e95a97c2b4
1 in β†’ 1 out8.3145 XPM116 B
ANSXnLY2…Sd25TjkD
5c2276f36318ff…d8137d69bf5bdb
3 in β†’ 1 out0.0107 XPM490 B
AFz3BYRc…iwykYJRA
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.

3.204 Γ— 10⁹⁸(99-digit number)
32046156511114933708…97654646319719383040
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
3.204 Γ— 10⁹⁸(99-digit number)
32046156511114933708…97654646319719383039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.204 Γ— 10⁹⁸(99-digit number)
32046156511114933708…97654646319719383041
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
6.409 Γ— 10⁹⁸(99-digit number)
64092313022229867416…95309292639438766079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.409 Γ— 10⁹⁸(99-digit number)
64092313022229867416…95309292639438766081
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
1.281 Γ— 10⁹⁹(100-digit number)
12818462604445973483…90618585278877532159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.281 Γ— 10⁹⁹(100-digit number)
12818462604445973483…90618585278877532161
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
2.563 Γ— 10⁹⁹(100-digit number)
25636925208891946966…81237170557755064319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.563 Γ— 10⁹⁹(100-digit number)
25636925208891946966…81237170557755064321
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
5.127 Γ— 10⁹⁹(100-digit number)
51273850417783893933…62474341115510128639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.127 Γ— 10⁹⁹(100-digit number)
51273850417783893933…62474341115510128641
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 840774

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 2dcea2d67468fb44a437da60a8d9a83c16a32596f33259c119e8baff0aa7f62a

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 #840,774 on Chainz β†—
Circulating Supply:58,007,292 XPMΒ·at block #6,845,355 Β· updates every 60s
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