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Home/Chain Registry/Block #1,408,540

Block #1,408,540

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2016, 9:43:47 AM Β· Difficulty 10.8044 Β· 5,434,512 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
75cc57a623b4abefeefc0a8a8ac5f4c82be07623e253c4a1aaae0939d4776d1d
View on Chainz β†—

Difficulty

10.804445

Transactions

1

Size

200 B

Version

2

Bits

0acdf01c

Nonce

656,311,603

Timestamp

1/11/2016, 9:43:47 AM

Confirmations

5,434,512

Merkle Root

ff5a6facc7b089f04fe19af65fa8074871e786f8de345f28bf73b5f65c638e0d
Transactions (1)
Coinbaseff5a6facc7b089…73b5f65c638e0d
1 in β†’ 1 out8.5500 XPM109 B
AX7GfJMS…d9GTM6na
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.

1.436 Γ— 10⁹⁸(99-digit number)
14361657126274204790…85066137036806553600
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
1.436 Γ— 10⁹⁸(99-digit number)
14361657126274204790…85066137036806553599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.436 Γ— 10⁹⁸(99-digit number)
14361657126274204790…85066137036806553601
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
2.872 Γ— 10⁹⁸(99-digit number)
28723314252548409580…70132274073613107199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.872 Γ— 10⁹⁸(99-digit number)
28723314252548409580…70132274073613107201
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
5.744 Γ— 10⁹⁸(99-digit number)
57446628505096819160…40264548147226214399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.744 Γ— 10⁹⁸(99-digit number)
57446628505096819160…40264548147226214401
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
1.148 Γ— 10⁹⁹(100-digit number)
11489325701019363832…80529096294452428799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.148 Γ— 10⁹⁹(100-digit number)
11489325701019363832…80529096294452428801
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
2.297 Γ— 10⁹⁹(100-digit number)
22978651402038727664…61058192588904857599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.297 Γ— 10⁹⁹(100-digit number)
22978651402038727664…61058192588904857601
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 1408540

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 75cc57a623b4abefeefc0a8a8ac5f4c82be07623e253c4a1aaae0939d4776d1d

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 #1,408,540 on Chainz β†—
Circulating Supply:57,988,774 XPMΒ·at block #6,843,051 Β· updates every 60s
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