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Home/Chain Registry/Block #1,610,584

Block #1,610,584

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/2/2016, 5:51:02 AM Β· Difficulty 10.6080 Β· 5,231,327 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5d859b5a50f052da24d733ce50f473c37850709de0dfdc38c56be5676cab99c5
View on Chainz β†—

Difficulty

10.607997

Transactions

1

Size

199 B

Version

2

Bits

0a9ba5b4

Nonce

1,141,222,220

Timestamp

6/2/2016, 5:51:02 AM

Confirmations

5,231,327

Merkle Root

06e5f6ab3b4b9a02370a479842063e973b17d4d56ce1fb673513c8be9cf70b70
Transactions (1)
Coinbase06e5f6ab3b4b9a…13c8be9cf70b70
1 in β†’ 1 out8.8700 XPM109 B
APKMs5Jr…RHQVWCPn
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.

1.588 Γ— 10⁹⁴(95-digit number)
15881232535728838688…65313473320914013920
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
1.588 Γ— 10⁹⁴(95-digit number)
15881232535728838688…65313473320914013919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.588 Γ— 10⁹⁴(95-digit number)
15881232535728838688…65313473320914013921
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
3.176 Γ— 10⁹⁴(95-digit number)
31762465071457677377…30626946641828027839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.176 Γ— 10⁹⁴(95-digit number)
31762465071457677377…30626946641828027841
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
6.352 Γ— 10⁹⁴(95-digit number)
63524930142915354754…61253893283656055679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.352 Γ— 10⁹⁴(95-digit number)
63524930142915354754…61253893283656055681
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
1.270 Γ— 10⁹⁡(96-digit number)
12704986028583070950…22507786567312111359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.270 Γ— 10⁹⁡(96-digit number)
12704986028583070950…22507786567312111361
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
2.540 Γ— 10⁹⁡(96-digit number)
25409972057166141901…45015573134624222719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.540 Γ— 10⁹⁡(96-digit number)
25409972057166141901…45015573134624222721
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 1610584

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 5d859b5a50f052da24d733ce50f473c37850709de0dfdc38c56be5676cab99c5

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 #1,610,584 on Chainz β†—
Circulating Supply:57,979,663 XPMΒ·at block #6,841,910 Β· updates every 60s
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