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Home/Chain Registry/Block #2,636,865

Block #2,636,865

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 5:57:47 PM Β· Difficulty 11.4062 Β· 4,195,016 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
65a038b921a4f4e7b80f7b7cf05f1cd6fdbb431ab8fb75e0b8d19c5a123b2c0c
View on Chainz β†—

Difficulty

11.406180

Transactions

2

Size

686 B

Version

2

Bits

0b67fb6f

Nonce

946,529,570

Timestamp

4/29/2018, 5:57:47 PM

Confirmations

4,195,016

Merkle Root

1d3b25d00dfb5f88ddf46da81945e0fd4ee29a54ea776c840df9bb05e78fbaef
Transactions (2)
Coinbaseb7dba677bfebdf…e708284bb413f3
1 in β†’ 1 out7.6800 XPM110 B
Adqah8zh…1WwoHJ9t
6bce5c023fa06e…957c4e65f1b4c0
3 in β†’ 2 out10.6000 XPM486 B
ALov4GXE…2gameYAfAP3EGrbe…xfBQWhVM
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.

3.250 Γ— 10⁹³(94-digit number)
32507271250106149967…70703685566533702000
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
3.250 Γ— 10⁹³(94-digit number)
32507271250106149967…70703685566533701999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.250 Γ— 10⁹³(94-digit number)
32507271250106149967…70703685566533702001
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
6.501 Γ— 10⁹³(94-digit number)
65014542500212299934…41407371133067403999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.501 Γ— 10⁹³(94-digit number)
65014542500212299934…41407371133067404001
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
1.300 Γ— 10⁹⁴(95-digit number)
13002908500042459986…82814742266134807999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.300 Γ— 10⁹⁴(95-digit number)
13002908500042459986…82814742266134808001
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
2.600 Γ— 10⁹⁴(95-digit number)
26005817000084919973…65629484532269615999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.600 Γ— 10⁹⁴(95-digit number)
26005817000084919973…65629484532269616001
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
5.201 Γ— 10⁹⁴(95-digit number)
52011634000169839947…31258969064539231999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.201 Γ— 10⁹⁴(95-digit number)
52011634000169839947…31258969064539232001
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
1.040 Γ— 10⁹⁡(96-digit number)
10402326800033967989…62517938129078463999
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 2636865

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 65a038b921a4f4e7b80f7b7cf05f1cd6fdbb431ab8fb75e0b8d19c5a123b2c0c

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 #2,636,865 on Chainz β†—
Circulating Supply:57,899,169 XPMΒ·at block #6,831,880 Β· updates every 60s
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