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Home/Chain Registry/Block #1,442,578

Block #1,442,578

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/4/2016, 6:43:56 PM Β· Difficulty 10.7599 Β· 5,371,526 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
45442654e4679d3fa6231fa3b294b0da0c64303461844f4ea91ad343fed21dfd
View on Chainz β†—

Difficulty

10.759947

Transactions

1

Size

199 B

Version

2

Bits

0ac28be1

Nonce

592,427,090

Timestamp

2/4/2016, 6:43:56 PM

Confirmations

5,371,526

Merkle Root

159e7d9803fbd3298712dd4f96beb4d9429ef008bb0d50a58a3ae520a1baa08a
Transactions (1)
Coinbase159e7d9803fbd3…3ae520a1baa08a
1 in β†’ 1 out8.6200 XPM109 B
ANQaNjZQ…UVPxs3fv
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.

4.006 Γ— 10⁹⁴(95-digit number)
40065214073648192911…90456305962505442080
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
4.006 Γ— 10⁹⁴(95-digit number)
40065214073648192911…90456305962505442079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.006 Γ— 10⁹⁴(95-digit number)
40065214073648192911…90456305962505442081
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
8.013 Γ— 10⁹⁴(95-digit number)
80130428147296385823…80912611925010884159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.013 Γ— 10⁹⁴(95-digit number)
80130428147296385823…80912611925010884161
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
1.602 Γ— 10⁹⁡(96-digit number)
16026085629459277164…61825223850021768319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.602 Γ— 10⁹⁡(96-digit number)
16026085629459277164…61825223850021768321
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
3.205 Γ— 10⁹⁡(96-digit number)
32052171258918554329…23650447700043536639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.205 Γ— 10⁹⁡(96-digit number)
32052171258918554329…23650447700043536641
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
6.410 Γ— 10⁹⁡(96-digit number)
64104342517837108658…47300895400087073279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.410 Γ— 10⁹⁡(96-digit number)
64104342517837108658…47300895400087073281
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 1442578

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 45442654e4679d3fa6231fa3b294b0da0c64303461844f4ea91ad343fed21dfd

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 #1,442,578 on Chainz β†—
Circulating Supply:57,756,915 XPMΒ·at block #6,814,103 Β· updates every 60s
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