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Home/Chain Registry/Block #2,611,451

Block #2,611,451

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/13/2018, 1:41:17 AM Β· Difficulty 11.2154 Β· 4,220,617 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
569775e39c04d9490a80df2a06735837fd524c4b4954036d0d145819f72a1a3c
View on Chainz β†—

Difficulty

11.215443

Transactions

1

Size

200 B

Version

2

Bits

0b37274d

Nonce

134,978,744

Timestamp

4/13/2018, 1:41:17 AM

Confirmations

4,220,617

Merkle Root

a30e3cd5a4900415346305a66dce88d02c00aec653da4ef8be24fbeb4e47ae27
Transactions (1)
Coinbasea30e3cd5a49004…24fbeb4e47ae27
1 in β†’ 1 out7.9400 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.

3.521 Γ— 10⁹⁴(95-digit number)
35213395634416465551…86730315827690242360
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
3.521 Γ— 10⁹⁴(95-digit number)
35213395634416465551…86730315827690242359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.521 Γ— 10⁹⁴(95-digit number)
35213395634416465551…86730315827690242361
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
7.042 Γ— 10⁹⁴(95-digit number)
70426791268832931103…73460631655380484719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.042 Γ— 10⁹⁴(95-digit number)
70426791268832931103…73460631655380484721
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
1.408 Γ— 10⁹⁡(96-digit number)
14085358253766586220…46921263310760969439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.408 Γ— 10⁹⁡(96-digit number)
14085358253766586220…46921263310760969441
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
2.817 Γ— 10⁹⁡(96-digit number)
28170716507533172441…93842526621521938879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.817 Γ— 10⁹⁡(96-digit number)
28170716507533172441…93842526621521938881
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
5.634 Γ— 10⁹⁡(96-digit number)
56341433015066344882…87685053243043877759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.634 Γ— 10⁹⁡(96-digit number)
56341433015066344882…87685053243043877761
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
1.126 Γ— 10⁹⁢(97-digit number)
11268286603013268976…75370106486087755519
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 2611451

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 569775e39c04d9490a80df2a06735837fd524c4b4954036d0d145819f72a1a3c

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 #2,611,451 on Chainz β†—
Circulating Supply:57,900,669 XPMΒ·at block #6,832,067 Β· updates every 60s
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