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Home/Chain Registry/Block #1,633,993

Block #1,633,993

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/18/2016, 1:41:54 PM Β· Difficulty 10.6009 Β· 5,190,491 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fab1a2cc41417ea1158bffd7268a328cb6c136a20e10c603ccbe011a1cc987b4
View on Chainz β†—

Difficulty

10.600923

Transactions

1

Size

200 B

Version

2

Bits

0a99d618

Nonce

1,068,323,810

Timestamp

6/18/2016, 1:41:54 PM

Confirmations

5,190,491

Merkle Root

03366348aaf53301ee013021e1fcc4bd57985d3d94eda63d67a113edaed64cd8
Transactions (1)
Coinbase03366348aaf533…a113edaed64cd8
1 in β†’ 1 out8.8800 XPM110 B
AXmKk8Vm…3sbDJJwz
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.

1.195 Γ— 10⁹⁡(96-digit number)
11953237609459754648…35297228435089829760
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
1.195 Γ— 10⁹⁡(96-digit number)
11953237609459754648…35297228435089829759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.195 Γ— 10⁹⁡(96-digit number)
11953237609459754648…35297228435089829761
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
2.390 Γ— 10⁹⁡(96-digit number)
23906475218919509297…70594456870179659519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.390 Γ— 10⁹⁡(96-digit number)
23906475218919509297…70594456870179659521
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
4.781 Γ— 10⁹⁡(96-digit number)
47812950437839018595…41188913740359319039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.781 Γ— 10⁹⁡(96-digit number)
47812950437839018595…41188913740359319041
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
9.562 Γ— 10⁹⁡(96-digit number)
95625900875678037191…82377827480718638079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.562 Γ— 10⁹⁡(96-digit number)
95625900875678037191…82377827480718638081
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
1.912 Γ— 10⁹⁢(97-digit number)
19125180175135607438…64755654961437276159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.912 Γ— 10⁹⁢(97-digit number)
19125180175135607438…64755654961437276161
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 1633993

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 fab1a2cc41417ea1158bffd7268a328cb6c136a20e10c603ccbe011a1cc987b4

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 #1,633,993 on Chainz β†—
Circulating Supply:57,839,943 XPMΒ·at block #6,824,483 Β· updates every 60s
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