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Home/Chain Registry/Block #2,488,334

Block #2,488,334

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/24/2018, 5:28:53 PM Β· Difficulty 10.9698 Β· 4,356,284 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d5da187d36e243d48341c27e58f3f2267032bc51c69b48324ed1fda2ffb9f85d
View on Chainz β†—

Difficulty

10.969808

Transactions

1

Size

199 B

Version

2

Bits

0af8454f

Nonce

394,069,639

Timestamp

1/24/2018, 5:28:53 PM

Confirmations

4,356,284

Merkle Root

b4318ff0c3cf02d1ea8f2047c68d285daa72f161016c6f8eee05051016ea38df
Transactions (1)
Coinbaseb4318ff0c3cf02…05051016ea38df
1 in β†’ 1 out8.3000 XPM109 B
AVJ9jGzG…a5RBYDyt
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.

4.695 Γ— 10⁹⁡(96-digit number)
46958212822769046602…22524776889609156160
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
4.695 Γ— 10⁹⁡(96-digit number)
46958212822769046602…22524776889609156159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.695 Γ— 10⁹⁡(96-digit number)
46958212822769046602…22524776889609156161
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
9.391 Γ— 10⁹⁡(96-digit number)
93916425645538093204…45049553779218312319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.391 Γ— 10⁹⁡(96-digit number)
93916425645538093204…45049553779218312321
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
1.878 Γ— 10⁹⁢(97-digit number)
18783285129107618640…90099107558436624639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.878 Γ— 10⁹⁢(97-digit number)
18783285129107618640…90099107558436624641
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
3.756 Γ— 10⁹⁢(97-digit number)
37566570258215237281…80198215116873249279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.756 Γ— 10⁹⁢(97-digit number)
37566570258215237281…80198215116873249281
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
7.513 Γ— 10⁹⁢(97-digit number)
75133140516430474563…60396430233746498559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.513 Γ— 10⁹⁢(97-digit number)
75133140516430474563…60396430233746498561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.502 Γ— 10⁹⁷(98-digit number)
15026628103286094912…20792860467492997119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2488334

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 d5da187d36e243d48341c27e58f3f2267032bc51c69b48324ed1fda2ffb9f85d

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 #2,488,334 on Chainz β†—
Circulating Supply:58,001,347 XPMΒ·at block #6,844,617 Β· updates every 60s
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