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Block #422,765

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/28/2014, 12:47:04 AM Β· Difficulty 10.3660 Β· 6,373,694 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b721f5d0e899aeefc34ed0333e412762e20134eb3aaa64acbf90a2235d002d49
View on Chainz β†—

Height

#422,765

Difficulty

10.366049

Transactions

1

Size

201 B

Version

2

Bits

0a5db567

Nonce

156,090

Timestamp

2/28/2014, 12:47:04 AM

Confirmations

6,373,694

Merkle Root

2f269f305051ce988afd079592b2fce586a5413fd2edd4718a72a2daff067282
Transactions (1)
Coinbase2f269f305051ce…72a2daff067282
1 in β†’ 1 out9.2900 XPM109 B
ASgyCPjz…CRhPm5uB
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.

2.406 Γ— 10⁹⁹(100-digit number)
24067797990727251032…01943933105315225600
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
2.406 Γ— 10⁹⁹(100-digit number)
24067797990727251032…01943933105315225599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.406 Γ— 10⁹⁹(100-digit number)
24067797990727251032…01943933105315225601
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
4.813 Γ— 10⁹⁹(100-digit number)
48135595981454502065…03887866210630451199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.813 Γ— 10⁹⁹(100-digit number)
48135595981454502065…03887866210630451201
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
9.627 Γ— 10⁹⁹(100-digit number)
96271191962909004131…07775732421260902399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.627 Γ— 10⁹⁹(100-digit number)
96271191962909004131…07775732421260902401
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
1.925 Γ— 10¹⁰⁰(101-digit number)
19254238392581800826…15551464842521804799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.925 Γ— 10¹⁰⁰(101-digit number)
19254238392581800826…15551464842521804801
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
3.850 Γ— 10¹⁰⁰(101-digit number)
38508476785163601652…31102929685043609599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.850 Γ— 10¹⁰⁰(101-digit number)
38508476785163601652…31102929685043609601
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 422765

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 b721f5d0e899aeefc34ed0333e412762e20134eb3aaa64acbf90a2235d002d49

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 #422,765 on Chainz β†—
Circulating Supply:57,615,668 XPMΒ·at block #6,796,458 Β· updates every 60s
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