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Home/Chain Registry/Block #2,158,495

Block #2,158,495

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/13/2017, 2:59:39 AM Β· Difficulty 10.9050 Β· 4,674,627 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
39000344a6e02301d4511967947d73104ee66a7b08aa14c2f67fde8d9cd45c5e
View on Chainz β†—

Difficulty

10.905027

Transactions

2

Size

1.98 KB

Version

2

Bits

0ae7afd6

Nonce

91,336,080

Timestamp

6/13/2017, 2:59:39 AM

Confirmations

4,674,627

Merkle Root

18a1eb73ab48a30b6babd72bbe38ecb1cf630501c6053a8602d71eaa3f8e6a15
Transactions (2)
Coinbaseabecf2a6fd0b40…b3c9480bbdca91
1 in β†’ 1 out8.4200 XPM109 B
Adaf7y2D…Nxp2hChE
dc472c227e8946…a865129eeab176
12 in β†’ 1 out742.3233 XPM1.78 KB
ANR6yEBj…xx5Lorbw
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.

1.439 Γ— 10⁹⁸(99-digit number)
14397021215124092099…65093613720409210880
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
1.439 Γ— 10⁹⁸(99-digit number)
14397021215124092099…65093613720409210879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.439 Γ— 10⁹⁸(99-digit number)
14397021215124092099…65093613720409210881
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
2.879 Γ— 10⁹⁸(99-digit number)
28794042430248184199…30187227440818421759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.879 Γ— 10⁹⁸(99-digit number)
28794042430248184199…30187227440818421761
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
5.758 Γ— 10⁹⁸(99-digit number)
57588084860496368399…60374454881636843519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.758 Γ— 10⁹⁸(99-digit number)
57588084860496368399…60374454881636843521
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
1.151 Γ— 10⁹⁹(100-digit number)
11517616972099273679…20748909763273687039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.151 Γ— 10⁹⁹(100-digit number)
11517616972099273679…20748909763273687041
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
2.303 Γ— 10⁹⁹(100-digit number)
23035233944198547359…41497819526547374079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.303 Γ— 10⁹⁹(100-digit number)
23035233944198547359…41497819526547374081
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 2158495

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 39000344a6e02301d4511967947d73104ee66a7b08aa14c2f67fde8d9cd45c5e

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 #2,158,495 on Chainz β†—
Circulating Supply:57,909,152 XPMΒ·at block #6,833,121 Β· updates every 60s
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