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Home/Chain Registry/Block #2,540,809

Block #2,540,809

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/27/2018, 11:29:23 AM Β· Difficulty 10.9871 Β· 4,297,538 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
64cb81b8a2b16086b233293e951d95a3c8efc9df7ef243b5c09b1ecb21bb45fe
View on Chainz β†—

Difficulty

10.987116

Transactions

1

Size

199 B

Version

2

Bits

0afcb3a5

Nonce

338,473,722

Timestamp

2/27/2018, 11:29:23 AM

Confirmations

4,297,538

Merkle Root

771b756a6a18edefc5ccf3e35274d6f10499daee4f8249e62bfa4ff2dcf4cb23
Transactions (1)
Coinbase771b756a6a18ed…fa4ff2dcf4cb23
1 in β†’ 1 out8.2700 XPM110 B
AJvdMTR8…8vF27trq
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.

2.036 Γ— 10⁹²(93-digit number)
20366163706022404060…39304148621339507680
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
2.036 Γ— 10⁹²(93-digit number)
20366163706022404060…39304148621339507679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.036 Γ— 10⁹²(93-digit number)
20366163706022404060…39304148621339507681
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
4.073 Γ— 10⁹²(93-digit number)
40732327412044808121…78608297242679015359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.073 Γ— 10⁹²(93-digit number)
40732327412044808121…78608297242679015361
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
8.146 Γ— 10⁹²(93-digit number)
81464654824089616242…57216594485358030719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.146 Γ— 10⁹²(93-digit number)
81464654824089616242…57216594485358030721
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
1.629 Γ— 10⁹³(94-digit number)
16292930964817923248…14433188970716061439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.629 Γ— 10⁹³(94-digit number)
16292930964817923248…14433188970716061441
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
3.258 Γ— 10⁹³(94-digit number)
32585861929635846496…28866377941432122879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.258 Γ— 10⁹³(94-digit number)
32585861929635846496…28866377941432122881
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
6.517 Γ— 10⁹³(94-digit number)
65171723859271692993…57732755882864245759
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 2540809

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 64cb81b8a2b16086b233293e951d95a3c8efc9df7ef243b5c09b1ecb21bb45fe

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 #2,540,809 on Chainz β†—
Circulating Supply:57,951,045 XPMΒ·at block #6,838,346 Β· updates every 60s
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