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Home/Chain Registry/Block #2,635,750

Block #2,635,750

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 8:33:30 AM Β· Difficulty 11.3376 Β· 4,205,717 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ec1edc29d7642e2371fef2badcab6afb4440fe1bf310be44c6e188d5a49b1a1b
View on Chainz β†—

Difficulty

11.337560

Transactions

1

Size

199 B

Version

2

Bits

0b566a55

Nonce

63,992,125

Timestamp

4/29/2018, 8:33:30 AM

Confirmations

4,205,717

Merkle Root

df44b099cee780cd1efdda3889c9e81659cb1a14dcaaf9a8e8ee6640efa47dd7
Transactions (1)
Coinbasedf44b099cee780…ee6640efa47dd7
1 in β†’ 1 out7.7700 XPM110 B
Adqah8zh…1WwoHJ9t
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.

5.753 Γ— 10⁹²(93-digit number)
57537129266507703451…89995274662669473920
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
5.753 Γ— 10⁹²(93-digit number)
57537129266507703451…89995274662669473919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.753 Γ— 10⁹²(93-digit number)
57537129266507703451…89995274662669473921
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
1.150 Γ— 10⁹³(94-digit number)
11507425853301540690…79990549325338947839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.150 Γ— 10⁹³(94-digit number)
11507425853301540690…79990549325338947841
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
2.301 Γ— 10⁹³(94-digit number)
23014851706603081380…59981098650677895679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.301 Γ— 10⁹³(94-digit number)
23014851706603081380…59981098650677895681
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
4.602 Γ— 10⁹³(94-digit number)
46029703413206162761…19962197301355791359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.602 Γ— 10⁹³(94-digit number)
46029703413206162761…19962197301355791361
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
9.205 Γ— 10⁹³(94-digit number)
92059406826412325522…39924394602711582719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.205 Γ— 10⁹³(94-digit number)
92059406826412325522…39924394602711582721
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
1.841 Γ— 10⁹⁴(95-digit number)
18411881365282465104…79848789205423165439
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 2635750

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 ec1edc29d7642e2371fef2badcab6afb4440fe1bf310be44c6e188d5a49b1a1b

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 #2,635,750 on Chainz β†—
Circulating Supply:57,976,110 XPMΒ·at block #6,841,466 Β· updates every 60s
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