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Home/Chain Registry/Block #2,831,648

Block #2,831,648

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2018, 11:38:22 AM Β· Difficulty 11.7175 Β· 4,007,385 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4edfa6cdb336394605cea43bb75244ad8ec462d44e69367748e159dd069d9697
View on Chainz β†—

Difficulty

11.717516

Transactions

1

Size

200 B

Version

2

Bits

0bb7af1f

Nonce

667,564,502

Timestamp

9/9/2018, 11:38:22 AM

Confirmations

4,007,385

Merkle Root

37cc6ecfd216cb97700535a8ff42debcd8742ad3daa1f51731194390a24c07dc
Transactions (1)
Coinbase37cc6ecfd216cb…194390a24c07dc
1 in β†’ 1 out7.2700 XPM110 B
AWYgd97T…jzNouCJW
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.

3.738 Γ— 10⁹³(94-digit number)
37380672557321783212…12402346381409318400
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
3.738 Γ— 10⁹³(94-digit number)
37380672557321783212…12402346381409318399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.738 Γ— 10⁹³(94-digit number)
37380672557321783212…12402346381409318401
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
7.476 Γ— 10⁹³(94-digit number)
74761345114643566425…24804692762818636799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.476 Γ— 10⁹³(94-digit number)
74761345114643566425…24804692762818636801
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
1.495 Γ— 10⁹⁴(95-digit number)
14952269022928713285…49609385525637273599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.495 Γ— 10⁹⁴(95-digit number)
14952269022928713285…49609385525637273601
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
2.990 Γ— 10⁹⁴(95-digit number)
29904538045857426570…99218771051274547199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.990 Γ— 10⁹⁴(95-digit number)
29904538045857426570…99218771051274547201
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
5.980 Γ— 10⁹⁴(95-digit number)
59809076091714853140…98437542102549094399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.980 Γ— 10⁹⁴(95-digit number)
59809076091714853140…98437542102549094401
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
1.196 Γ— 10⁹⁡(96-digit number)
11961815218342970628…96875084205098188799
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 2831648

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 4edfa6cdb336394605cea43bb75244ad8ec462d44e69367748e159dd069d9697

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 #2,831,648 on Chainz β†—
Circulating Supply:57,956,531 XPMΒ·at block #6,839,032 Β· updates every 60s
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