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Home/Chain Registry/Block #2,471,708

Block #2,471,708

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/13/2018, 9:57:45 PM Β· Difficulty 10.9622 Β· 4,371,595 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f068b57db8f2a996b98207c28e7361ade7e7d17cc59743bce6a8b3b33e4aad2c
View on Chainz β†—

Difficulty

10.962231

Transactions

1

Size

200 B

Version

2

Bits

0af654bd

Nonce

1,164,401,031

Timestamp

1/13/2018, 9:57:45 PM

Confirmations

4,371,595

Merkle Root

f2b18d013c738752b34db6c0c5c419992dba3d5bd1d6d6c7a2b02f309181930e
Transactions (1)
Coinbasef2b18d013c7387…b02f309181930e
1 in β†’ 1 out8.3100 XPM109 B
ARpDZbiU…UXAjB2Af
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.

5.707 Γ— 10⁹⁢(97-digit number)
57075858319329950008…76032604879988305920
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
5.707 Γ— 10⁹⁢(97-digit number)
57075858319329950008…76032604879988305919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.707 Γ— 10⁹⁢(97-digit number)
57075858319329950008…76032604879988305921
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
1.141 Γ— 10⁹⁷(98-digit number)
11415171663865990001…52065209759976611839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.141 Γ— 10⁹⁷(98-digit number)
11415171663865990001…52065209759976611841
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
2.283 Γ— 10⁹⁷(98-digit number)
22830343327731980003…04130419519953223679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.283 Γ— 10⁹⁷(98-digit number)
22830343327731980003…04130419519953223681
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
4.566 Γ— 10⁹⁷(98-digit number)
45660686655463960007…08260839039906447359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.566 Γ— 10⁹⁷(98-digit number)
45660686655463960007…08260839039906447361
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
9.132 Γ— 10⁹⁷(98-digit number)
91321373310927920014…16521678079812894719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.132 Γ— 10⁹⁷(98-digit number)
91321373310927920014…16521678079812894721
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 2471708

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 f068b57db8f2a996b98207c28e7361ade7e7d17cc59743bce6a8b3b33e4aad2c

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 #2,471,708 on Chainz β†—
Circulating Supply:57,990,789 XPMΒ·at block #6,843,302 Β· updates every 60s
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