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Home/Chain Registry/Block #2,557,474

Block #2,557,474

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/9/2018, 7:17:17 PM Β· Difficulty 10.9914 Β· 4,274,314 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8db74a45189499e414e76869a59f1f3da38b338bb74db50d4f82295ae83e34bd
View on Chainz β†—

Difficulty

10.991384

Transactions

1

Size

200 B

Version

2

Bits

0afdcb54

Nonce

1,171,873,310

Timestamp

3/9/2018, 7:17:17 PM

Confirmations

4,274,314

Merkle Root

89471a7b16f3fd321dc03f1be747dbbffd420647fc859f8e11b7f7242f8936de
Transactions (1)
Coinbase89471a7b16f3fd…b7f7242f8936de
1 in β†’ 1 out8.2600 XPM110 B
AW1yMDyo…paYr752x
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.

2.999 Γ— 10⁹⁴(95-digit number)
29990428267252839445…77759570030673553920
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
2.999 Γ— 10⁹⁴(95-digit number)
29990428267252839445…77759570030673553919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.999 Γ— 10⁹⁴(95-digit number)
29990428267252839445…77759570030673553921
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
5.998 Γ— 10⁹⁴(95-digit number)
59980856534505678890…55519140061347107839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.998 Γ— 10⁹⁴(95-digit number)
59980856534505678890…55519140061347107841
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
1.199 Γ— 10⁹⁡(96-digit number)
11996171306901135778…11038280122694215679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.199 Γ— 10⁹⁡(96-digit number)
11996171306901135778…11038280122694215681
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
2.399 Γ— 10⁹⁡(96-digit number)
23992342613802271556…22076560245388431359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.399 Γ— 10⁹⁡(96-digit number)
23992342613802271556…22076560245388431361
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
4.798 Γ— 10⁹⁡(96-digit number)
47984685227604543112…44153120490776862719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.798 Γ— 10⁹⁡(96-digit number)
47984685227604543112…44153120490776862721
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
9.596 Γ— 10⁹⁡(96-digit number)
95969370455209086225…88306240981553725439
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 2557474

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 8db74a45189499e414e76869a59f1f3da38b338bb74db50d4f82295ae83e34bd

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 #2,557,474 on Chainz β†—
Circulating Supply:57,898,418 XPMΒ·at block #6,831,787 Β· updates every 60s
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