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Block #526,916

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2014, 4:42:26 PM Β· Difficulty 10.8837 Β· 6,297,596 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa3c63c55bb963be06f88aac4465f46c5b42a3333fcb530879d197fe74c5fa33
View on Chainz β†—

Height

#526,916

Difficulty

10.883697

Transactions

1

Size

197 B

Version

2

Bits

0ae239f3

Nonce

1,245,328,991

Timestamp

5/5/2014, 4:42:26 PM

Confirmations

6,297,596

Merkle Root

98160a7755d1a057a6e0877870056daa6991b2e9a6d2c61762882d1fbb00765d
Transactions (1)
Coinbase98160a7755d1a0…882d1fbb00765d
1 in β†’ 1 out8.4300 XPM109 B
Ac9rEx9Y…NSD82EBw
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.

2.714 Γ— 10⁸⁹(90-digit number)
27146665977141927600…40394146320127459510
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
2.714 Γ— 10⁸⁹(90-digit number)
27146665977141927600…40394146320127459509
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.714 Γ— 10⁸⁹(90-digit number)
27146665977141927600…40394146320127459511
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
5.429 Γ— 10⁸⁹(90-digit number)
54293331954283855200…80788292640254919019
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.429 Γ— 10⁸⁹(90-digit number)
54293331954283855200…80788292640254919021
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
1.085 Γ— 10⁹⁰(91-digit number)
10858666390856771040…61576585280509838039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.085 Γ— 10⁹⁰(91-digit number)
10858666390856771040…61576585280509838041
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
2.171 Γ— 10⁹⁰(91-digit number)
21717332781713542080…23153170561019676079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.171 Γ— 10⁹⁰(91-digit number)
21717332781713542080…23153170561019676081
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
4.343 Γ— 10⁹⁰(91-digit number)
43434665563427084160…46306341122039352159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.343 Γ— 10⁹⁰(91-digit number)
43434665563427084160…46306341122039352161
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 526916

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 fa3c63c55bb963be06f88aac4465f46c5b42a3333fcb530879d197fe74c5fa33

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 #526,916 on Chainz β†—
Circulating Supply:57,840,157 XPMΒ·at block #6,824,511 Β· updates every 60s
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