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Home/Chain Registry/Block #1,449,353

Block #1,449,353

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/9/2016, 1:45:59 PM Β· Difficulty 10.7541 Β· 5,389,853 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a06c865881ce8bfc54643415d0f6fa95015279ccf130a570b5a299f6fc6da64c
View on Chainz β†—

Difficulty

10.754075

Transactions

1

Size

202 B

Version

2

Bits

0ac10b0d

Nonce

1,552,278,684

Timestamp

2/9/2016, 1:45:59 PM

Confirmations

5,389,853

Merkle Root

88964d710d013cdc74648a819df269fe69d1e40679fbc22254d5ba0b7cc64de1
Transactions (1)
Coinbase88964d710d013c…d5ba0b7cc64de1
1 in β†’ 1 out8.6300 XPM110 B
AbHwmpCi…MUW7mwit
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.

6.786 Γ— 10⁹⁸(99-digit number)
67866990774704138075…68857177917219799040
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
6.786 Γ— 10⁹⁸(99-digit number)
67866990774704138075…68857177917219799039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.786 Γ— 10⁹⁸(99-digit number)
67866990774704138075…68857177917219799041
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
1.357 Γ— 10⁹⁹(100-digit number)
13573398154940827615…37714355834439598079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.357 Γ— 10⁹⁹(100-digit number)
13573398154940827615…37714355834439598081
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
2.714 Γ— 10⁹⁹(100-digit number)
27146796309881655230…75428711668879196159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.714 Γ— 10⁹⁹(100-digit number)
27146796309881655230…75428711668879196161
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
5.429 Γ— 10⁹⁹(100-digit number)
54293592619763310460…50857423337758392319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.429 Γ— 10⁹⁹(100-digit number)
54293592619763310460…50857423337758392321
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
1.085 Γ— 10¹⁰⁰(101-digit number)
10858718523952662092…01714846675516784639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.085 Γ— 10¹⁰⁰(101-digit number)
10858718523952662092…01714846675516784641
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 1449353

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 a06c865881ce8bfc54643415d0f6fa95015279ccf130a570b5a299f6fc6da64c

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 #1,449,353 on Chainz β†—
Circulating Supply:57,957,928 XPMΒ·at block #6,839,205 Β· updates every 60s
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