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Home/Chain Registry/Block #2,468,551

Block #2,468,551

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2018, 9:49:35 PM Β· Difficulty 10.9601 Β· 4,374,396 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5ce36f5c6cc22509d8d8212e11d622180b7654a035f07ae7869c5dc63353938a
View on Chainz β†—

Difficulty

10.960068

Transactions

1

Size

201 B

Version

2

Bits

0af5c709

Nonce

135,422,738

Timestamp

1/11/2018, 9:49:35 PM

Confirmations

4,374,396

Merkle Root

fae7b2bab147aa684720a7bb6b6b827f1d8f7166c8be3a100c09bfe47a3b873b
Transactions (1)
Coinbasefae7b2bab147aa…09bfe47a3b873b
1 in β†’ 1 out8.3100 XPM110 B
AJ32UnKX…fE4pLxUm
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.

9.367 Γ— 10⁹⁢(97-digit number)
93676931157533057923…13563107045795911680
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
9.367 Γ— 10⁹⁢(97-digit number)
93676931157533057923…13563107045795911679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.367 Γ— 10⁹⁢(97-digit number)
93676931157533057923…13563107045795911681
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
1.873 Γ— 10⁹⁷(98-digit number)
18735386231506611584…27126214091591823359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.873 Γ— 10⁹⁷(98-digit number)
18735386231506611584…27126214091591823361
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
3.747 Γ— 10⁹⁷(98-digit number)
37470772463013223169…54252428183183646719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.747 Γ— 10⁹⁷(98-digit number)
37470772463013223169…54252428183183646721
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
7.494 Γ— 10⁹⁷(98-digit number)
74941544926026446338…08504856366367293439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.494 Γ— 10⁹⁷(98-digit number)
74941544926026446338…08504856366367293441
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
1.498 Γ— 10⁹⁸(99-digit number)
14988308985205289267…17009712732734586879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.498 Γ— 10⁹⁸(99-digit number)
14988308985205289267…17009712732734586881
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 2468551

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 5ce36f5c6cc22509d8d8212e11d622180b7654a035f07ae7869c5dc63353938a

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 #2,468,551 on Chainz β†—
Circulating Supply:57,987,927 XPMΒ·at block #6,842,946 Β· updates every 60s
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