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Block #453,666

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/21/2014, 11:09:21 AM Β· Difficulty 10.3881 Β· 6,344,735 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a5f1c02c6f969e5e7131d10355c3dedb972ec7d88d95a98a5689be5c16535620
View on Chainz β†—

Height

#453,666

Difficulty

10.388078

Transactions

1

Size

202 B

Version

2

Bits

0a63590e

Nonce

228,849

Timestamp

3/21/2014, 11:09:21 AM

Confirmations

6,344,735

Merkle Root

530e86e1d4e44f5d45bfdbeab630b65758bcdd6124c1d3d6577f5e204e1a37eb
Transactions (1)
Coinbase530e86e1d4e44f…7f5e204e1a37eb
1 in β†’ 1 out9.2500 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.624 Γ— 10⁹⁹(100-digit number)
36241797331627132668…79605010617829458600
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
3.624 Γ— 10⁹⁹(100-digit number)
36241797331627132668…79605010617829458599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.624 Γ— 10⁹⁹(100-digit number)
36241797331627132668…79605010617829458601
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
7.248 Γ— 10⁹⁹(100-digit number)
72483594663254265337…59210021235658917199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.248 Γ— 10⁹⁹(100-digit number)
72483594663254265337…59210021235658917201
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
1.449 Γ— 10¹⁰⁰(101-digit number)
14496718932650853067…18420042471317834399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.449 Γ— 10¹⁰⁰(101-digit number)
14496718932650853067…18420042471317834401
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
2.899 Γ— 10¹⁰⁰(101-digit number)
28993437865301706134…36840084942635668799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.899 Γ— 10¹⁰⁰(101-digit number)
28993437865301706134…36840084942635668801
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
5.798 Γ— 10¹⁰⁰(101-digit number)
57986875730603412269…73680169885271337599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.798 Γ— 10¹⁰⁰(101-digit number)
57986875730603412269…73680169885271337601
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 453666

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 a5f1c02c6f969e5e7131d10355c3dedb972ec7d88d95a98a5689be5c16535620

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 #453,666 on Chainz β†—
Circulating Supply:57,631,217 XPMΒ·at block #6,798,400 Β· updates every 60s
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