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Home/Chain Registry/Block #2,642,067

Block #2,642,067

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 2:27:00 PM Β· Difficulty 11.6409 Β· 4,188,938 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
03cf7d1835bc0cb1638a973c288f045d8b1acf61e2ebf111580a0d5b70a8fc11
View on Chainz β†—

Difficulty

11.640874

Transactions

1

Size

200 B

Version

2

Bits

0ba4104c

Nonce

292,455,281

Timestamp

5/1/2018, 2:27:00 PM

Confirmations

4,188,938

Merkle Root

6bf782577436a7e1f9167420e0b130381021e6fbf1e7c31d999b43b374b7f27a
Transactions (1)
Coinbase6bf782577436a7…9b43b374b7f27a
1 in β†’ 1 out7.3700 XPM110 B
Ach1fHC8…teT85gs3
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.

1.255 Γ— 10⁹⁡(96-digit number)
12551601717885550987…56186238253833086600
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
1.255 Γ— 10⁹⁡(96-digit number)
12551601717885550987…56186238253833086599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.255 Γ— 10⁹⁡(96-digit number)
12551601717885550987…56186238253833086601
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
2.510 Γ— 10⁹⁡(96-digit number)
25103203435771101974…12372476507666173199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.510 Γ— 10⁹⁡(96-digit number)
25103203435771101974…12372476507666173201
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
5.020 Γ— 10⁹⁡(96-digit number)
50206406871542203948…24744953015332346399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.020 Γ— 10⁹⁡(96-digit number)
50206406871542203948…24744953015332346401
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
1.004 Γ— 10⁹⁢(97-digit number)
10041281374308440789…49489906030664692799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.004 Γ— 10⁹⁢(97-digit number)
10041281374308440789…49489906030664692801
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
2.008 Γ— 10⁹⁢(97-digit number)
20082562748616881579…98979812061329385599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.008 Γ— 10⁹⁢(97-digit number)
20082562748616881579…98979812061329385601
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
4.016 Γ— 10⁹⁢(97-digit number)
40165125497233763158…97959624122658771199
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 2642067

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 03cf7d1835bc0cb1638a973c288f045d8b1acf61e2ebf111580a0d5b70a8fc11

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 #2,642,067 on Chainz β†—
Circulating Supply:57,892,181 XPMΒ·at block #6,831,004 Β· updates every 60s
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