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Home/Chain Registry/Block #1,419,342

Block #1,419,342

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2016, 3:09:47 AM Β· Difficulty 10.7918 Β· 5,421,427 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bf95545016b3d89c324493414610e29e2a6de12f76813ac9b0a98dbb28f5dc3e
View on Chainz β†—

Difficulty

10.791813

Transactions

1

Size

201 B

Version

2

Bits

0acab43b

Nonce

896,655,811

Timestamp

1/19/2016, 3:09:47 AM

Confirmations

5,421,427

Merkle Root

da2ef8ca58b3b4a383bf34f5ca116974264d1b17c2fc5b77275e3aab2eda8e28
Transactions (1)
Coinbaseda2ef8ca58b3b4…5e3aab2eda8e28
1 in β†’ 1 out8.5700 XPM110 B
AXu8kqCR…5h9JLspR
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.

1.708 Γ— 10⁹⁢(97-digit number)
17083177754413316388…77302198742069555200
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
1.708 Γ— 10⁹⁢(97-digit number)
17083177754413316388…77302198742069555199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.708 Γ— 10⁹⁢(97-digit number)
17083177754413316388…77302198742069555201
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
3.416 Γ— 10⁹⁢(97-digit number)
34166355508826632776…54604397484139110399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.416 Γ— 10⁹⁢(97-digit number)
34166355508826632776…54604397484139110401
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
6.833 Γ— 10⁹⁢(97-digit number)
68332711017653265552…09208794968278220799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.833 Γ— 10⁹⁢(97-digit number)
68332711017653265552…09208794968278220801
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
1.366 Γ— 10⁹⁷(98-digit number)
13666542203530653110…18417589936556441599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.366 Γ— 10⁹⁷(98-digit number)
13666542203530653110…18417589936556441601
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
2.733 Γ— 10⁹⁷(98-digit number)
27333084407061306220…36835179873112883199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.733 Γ— 10⁹⁷(98-digit number)
27333084407061306220…36835179873112883201
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 1419342

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 bf95545016b3d89c324493414610e29e2a6de12f76813ac9b0a98dbb28f5dc3e

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 #1,419,342 on Chainz β†—
Circulating Supply:57,970,495 XPMΒ·at block #6,840,768 Β· updates every 60s
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