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Block #162,464

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 8:08:43 AM Β· Difficulty 9.8612 Β· 6,663,059 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1bc7aeb000015fa38df18e84d3e1e048cedc47a8ea891069c5c89fab0dd31738
View on Chainz β†—

Height

#162,464

Difficulty

9.861246

Transactions

1

Size

198 B

Version

2

Bits

09dc7aa4

Nonce

37,479

Timestamp

9/13/2013, 8:08:43 AM

Confirmations

6,663,059

Merkle Root

944a925b7a35c5e854816ce211b290ec9eb9bd1971fba56dbcf103b41ebce022
Transactions (1)
Coinbase944a925b7a35c5…f103b41ebce022
1 in β†’ 1 out10.2700 XPM109 B
ATfkLTJT…R6ZBdUL9
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.

6.029 Γ— 10⁹²(93-digit number)
60299999466383614096…76375942188632273200
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
6.029 Γ— 10⁹²(93-digit number)
60299999466383614096…76375942188632273199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.029 Γ— 10⁹²(93-digit number)
60299999466383614096…76375942188632273201
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
1.205 Γ— 10⁹³(94-digit number)
12059999893276722819…52751884377264546399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.205 Γ— 10⁹³(94-digit number)
12059999893276722819…52751884377264546401
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
2.411 Γ— 10⁹³(94-digit number)
24119999786553445638…05503768754529092799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.411 Γ— 10⁹³(94-digit number)
24119999786553445638…05503768754529092801
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
4.823 Γ— 10⁹³(94-digit number)
48239999573106891277…11007537509058185599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.823 Γ— 10⁹³(94-digit number)
48239999573106891277…11007537509058185601
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
9.647 Γ— 10⁹³(94-digit number)
96479999146213782555…22015075018116371199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 162464

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 1bc7aeb000015fa38df18e84d3e1e048cedc47a8ea891069c5c89fab0dd31738

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 #162,464 on Chainz β†—
Circulating Supply:57,848,280 XPMΒ·at block #6,825,522 Β· updates every 60s
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