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Home/Chain Registry/Block #1,375,044

Block #1,375,044

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/19/2015, 12:54:37 AM Β· Difficulty 10.8092 Β· 5,469,012 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
baceb5a0c3e682d0fcd39702db83c049edf03a79adc64064763b71f6f3952b9c
View on Chainz β†—

Difficulty

10.809211

Transactions

1

Size

200 B

Version

2

Bits

0acf287b

Nonce

1,481,759,489

Timestamp

12/19/2015, 12:54:37 AM

Confirmations

5,469,012

Merkle Root

0e5688d99487285636468691da20b57668721437836f9acae9dd72ee1e8d9bcf
Transactions (1)
Coinbase0e5688d9948728…dd72ee1e8d9bcf
1 in β†’ 1 out8.5500 XPM109 B
ASBbqMeh…WgAmFfey
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.

2.940 Γ— 10⁹⁷(98-digit number)
29404703703418863278…49955826663316848640
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
2.940 Γ— 10⁹⁷(98-digit number)
29404703703418863278…49955826663316848639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.940 Γ— 10⁹⁷(98-digit number)
29404703703418863278…49955826663316848641
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
5.880 Γ— 10⁹⁷(98-digit number)
58809407406837726556…99911653326633697279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.880 Γ— 10⁹⁷(98-digit number)
58809407406837726556…99911653326633697281
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
1.176 Γ— 10⁹⁸(99-digit number)
11761881481367545311…99823306653267394559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.176 Γ— 10⁹⁸(99-digit number)
11761881481367545311…99823306653267394561
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
2.352 Γ— 10⁹⁸(99-digit number)
23523762962735090622…99646613306534789119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.352 Γ— 10⁹⁸(99-digit number)
23523762962735090622…99646613306534789121
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
4.704 Γ— 10⁹⁸(99-digit number)
47047525925470181245…99293226613069578239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.704 Γ— 10⁹⁸(99-digit number)
47047525925470181245…99293226613069578241
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 1375044

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 baceb5a0c3e682d0fcd39702db83c049edf03a79adc64064763b71f6f3952b9c

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 #1,375,044 on Chainz β†—
Circulating Supply:57,996,819 XPMΒ·at block #6,844,055 Β· updates every 60s
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