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Home/Chain Registry/Block #1,428,715

Block #1,428,715

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/26/2016, 9:15:24 AM Β· Difficulty 10.7429 Β· 5,414,416 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
92a035023584e4a4d6e92bf809ffa38c165e78a8b4df6a55a07adb005020a507
View on Chainz β†—

Difficulty

10.742877

Transactions

1

Size

201 B

Version

2

Bits

0abe2d28

Nonce

179,644,977

Timestamp

1/26/2016, 9:15:24 AM

Confirmations

5,414,416

Merkle Root

a2cd24c1328bfc85a07c92bc46f06a48b518ea791cf9e4b932fd38afdc74e395
Transactions (1)
Coinbasea2cd24c1328bfc…fd38afdc74e395
1 in β†’ 1 out8.6500 XPM110 B
AJvyYcCW…eeMestFk
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.

1.156 Γ— 10⁹⁸(99-digit number)
11564264411687812921…82560611883008122880
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
1.156 Γ— 10⁹⁸(99-digit number)
11564264411687812921…82560611883008122879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.156 Γ— 10⁹⁸(99-digit number)
11564264411687812921…82560611883008122881
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
2.312 Γ— 10⁹⁸(99-digit number)
23128528823375625843…65121223766016245759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.312 Γ— 10⁹⁸(99-digit number)
23128528823375625843…65121223766016245761
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
4.625 Γ— 10⁹⁸(99-digit number)
46257057646751251687…30242447532032491519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.625 Γ— 10⁹⁸(99-digit number)
46257057646751251687…30242447532032491521
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
9.251 Γ— 10⁹⁸(99-digit number)
92514115293502503374…60484895064064983039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.251 Γ— 10⁹⁸(99-digit number)
92514115293502503374…60484895064064983041
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
1.850 Γ— 10⁹⁹(100-digit number)
18502823058700500674…20969790128129966079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.850 Γ— 10⁹⁹(100-digit number)
18502823058700500674…20969790128129966081
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 1428715

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 92a035023584e4a4d6e92bf809ffa38c165e78a8b4df6a55a07adb005020a507

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 #1,428,715 on Chainz β†—
Circulating Supply:57,989,411 XPMΒ·at block #6,843,130 Β· updates every 60s
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