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Home/Chain Registry/Block #3,181,555

Block #3,181,555

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/14/2019, 9:10:29 AM Β· Difficulty 11.2587 Β· 3,661,196 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
69cc9859bd9ef330cfc8319c52220c331c0c66521353d2cc93c3bc6bc2941bf7
View on Chainz β†—

Difficulty

11.258710

Transactions

1

Size

200 B

Version

2

Bits

0b423ad8

Nonce

466,443,369

Timestamp

5/14/2019, 9:10:29 AM

Confirmations

3,661,196

Merkle Root

949b226478335a38aaa72273c90313c33c5af1eda1201a8a696a4b770aa93320
Transactions (1)
Coinbase949b226478335a…6a4b770aa93320
1 in β†’ 1 out7.8800 XPM109 B
ARbm48qR…9xQc8DBX
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.

6.832 Γ— 10⁹⁷(98-digit number)
68320946640296641090…72624869336636948480
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
6.832 Γ— 10⁹⁷(98-digit number)
68320946640296641090…72624869336636948479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.832 Γ— 10⁹⁷(98-digit number)
68320946640296641090…72624869336636948481
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
1.366 Γ— 10⁹⁸(99-digit number)
13664189328059328218…45249738673273896959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.366 Γ— 10⁹⁸(99-digit number)
13664189328059328218…45249738673273896961
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
2.732 Γ— 10⁹⁸(99-digit number)
27328378656118656436…90499477346547793919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.732 Γ— 10⁹⁸(99-digit number)
27328378656118656436…90499477346547793921
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
5.465 Γ— 10⁹⁸(99-digit number)
54656757312237312872…80998954693095587839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.465 Γ— 10⁹⁸(99-digit number)
54656757312237312872…80998954693095587841
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
1.093 Γ— 10⁹⁹(100-digit number)
10931351462447462574…61997909386191175679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.093 Γ— 10⁹⁹(100-digit number)
10931351462447462574…61997909386191175681
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
2.186 Γ— 10⁹⁹(100-digit number)
21862702924894925148…23995818772382351359
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 3181555

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 69cc9859bd9ef330cfc8319c52220c331c0c66521353d2cc93c3bc6bc2941bf7

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 #3,181,555 on Chainz β†—
Circulating Supply:57,986,345 XPMΒ·at block #6,842,750 Β· updates every 60s
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