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Block #285,823

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2013, 3:43:23 PM Β· Difficulty 9.9848 Β· 6,529,093 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3717a697ec75f7a1ee558b7bc8cce162a8c3fc5fb2cb097835bdd053b3383c4c
View on Chainz β†—

Height

#285,823

Difficulty

9.984810

Transactions

1

Size

207 B

Version

2

Bits

09fc1c87

Nonce

3,413

Timestamp

11/30/2013, 3:43:23 PM

Confirmations

6,529,093

Merkle Root

17bf34936ee37e2d626b5ef23b11d34838bc841061e0eca66e7e3f0c7431c6c4
Transactions (1)
Coinbase17bf34936ee37e…7e3f0c7431c6c4
1 in β†’ 1 out10.0200 XPM116 B
AcLBm5Z9…S683d7c3
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.

6.769 Γ— 10⁹⁢(97-digit number)
67695538383096716509…73711139057608255650
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
6.769 Γ— 10⁹⁢(97-digit number)
67695538383096716509…73711139057608255649
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.769 Γ— 10⁹⁢(97-digit number)
67695538383096716509…73711139057608255651
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
1.353 Γ— 10⁹⁷(98-digit number)
13539107676619343301…47422278115216511299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.353 Γ— 10⁹⁷(98-digit number)
13539107676619343301…47422278115216511301
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
2.707 Γ— 10⁹⁷(98-digit number)
27078215353238686603…94844556230433022599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.707 Γ— 10⁹⁷(98-digit number)
27078215353238686603…94844556230433022601
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
5.415 Γ— 10⁹⁷(98-digit number)
54156430706477373207…89689112460866045199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.415 Γ— 10⁹⁷(98-digit number)
54156430706477373207…89689112460866045201
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
1.083 Γ— 10⁹⁸(99-digit number)
10831286141295474641…79378224921732090399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.083 Γ— 10⁹⁸(99-digit number)
10831286141295474641…79378224921732090401
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 285823

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 3717a697ec75f7a1ee558b7bc8cce162a8c3fc5fb2cb097835bdd053b3383c4c

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 #285,823 on Chainz β†—
Circulating Supply:57,763,420 XPMΒ·at block #6,814,915 Β· updates every 60s
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