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Block #2,406

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/8/2013, 7:59:24 PM Β· Difficulty 7.1603 Β· 6,797,924 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
41d1887f275eaaede65a075c8623ac4ddb062d9e4a376aaefeef49bfd56b6e35
View on Chainz β†—

Height

#2,406

Difficulty

7.160259

Transactions

1

Size

203 B

Version

2

Bits

072906c0

Nonce

202

Timestamp

7/8/2013, 7:59:24 PM

Confirmations

6,797,924

Merkle Root

287bf0672f8112b2f7ebb96c8fcb2cd61b9e2ab65f0b86b4bc7991d653b5b050
Transactions (1)
Coinbase287bf0672f8112…7991d653b5b050
1 in β†’ 1 out19.4800 XPM108 B
AGpLwH35…gWJu3vdc
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.

5.761 Γ— 10¹⁰⁡(106-digit number)
57610296227554716495…18802524524213805860
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
5.761 Γ— 10¹⁰⁡(106-digit number)
57610296227554716495…18802524524213805859
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.761 Γ— 10¹⁰⁡(106-digit number)
57610296227554716495…18802524524213805861
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
1.152 Γ— 10¹⁰⁢(107-digit number)
11522059245510943299…37605049048427611719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.152 Γ— 10¹⁰⁢(107-digit number)
11522059245510943299…37605049048427611721
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
2.304 Γ— 10¹⁰⁢(107-digit number)
23044118491021886598…75210098096855223439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.304 Γ— 10¹⁰⁢(107-digit number)
23044118491021886598…75210098096855223441
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
4.608 Γ— 10¹⁰⁢(107-digit number)
46088236982043773196…50420196193710446879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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
CommonChain length 7
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 2406

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 41d1887f275eaaede65a075c8623ac4ddb062d9e4a376aaefeef49bfd56b6e35

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 #2,406 on Chainz β†—
Circulating Supply:57,646,696 XPMΒ·at block #6,800,329 Β· updates every 60s
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