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Home/Chain Registry/Block #2,641,711

Block #2,641,711

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 11:17:51 AM Β· Difficulty 11.6288 Β· 4,189,224 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ea74c683d00f8783405e53bb94a864f2f5a144a77340553830fd64f65504bcc6
View on Chainz β†—

Difficulty

11.628835

Transactions

1

Size

201 B

Version

2

Bits

0ba0fb58

Nonce

225,505,746

Timestamp

5/1/2018, 11:17:51 AM

Confirmations

4,189,224

Merkle Root

4ba74721e2e2aad17f91480702f20a547a2122387e8d92a9840cde1c66878422
Transactions (1)
Coinbase4ba74721e2e2aa…0cde1c66878422
1 in β†’ 1 out7.3800 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.930 Γ— 10⁹⁷(98-digit number)
29308434972812416795…56014090771867893760
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
2.930 Γ— 10⁹⁷(98-digit number)
29308434972812416795…56014090771867893759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.930 Γ— 10⁹⁷(98-digit number)
29308434972812416795…56014090771867893761
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
5.861 Γ— 10⁹⁷(98-digit number)
58616869945624833591…12028181543735787519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.861 Γ— 10⁹⁷(98-digit number)
58616869945624833591…12028181543735787521
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
1.172 Γ— 10⁹⁸(99-digit number)
11723373989124966718…24056363087471575039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.172 Γ— 10⁹⁸(99-digit number)
11723373989124966718…24056363087471575041
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
2.344 Γ— 10⁹⁸(99-digit number)
23446747978249933436…48112726174943150079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.344 Γ— 10⁹⁸(99-digit number)
23446747978249933436…48112726174943150081
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
4.689 Γ— 10⁹⁸(99-digit number)
46893495956499866873…96225452349886300159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.689 Γ— 10⁹⁸(99-digit number)
46893495956499866873…96225452349886300161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.378 Γ— 10⁹⁸(99-digit number)
93786991912999733746…92450904699772600319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2641711

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 ea74c683d00f8783405e53bb94a864f2f5a144a77340553830fd64f65504bcc6

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 #2,641,711 on Chainz β†—
Circulating Supply:57,891,613 XPMΒ·at block #6,830,934 Β· updates every 60s
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