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Block #289,447

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/2/2013, 5:13:52 AM Β· Difficulty 9.9885 Β· 6,536,949 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca3364ebc84b7133ebeaa3334b397721a777636b6ae5459ff2a3ac0c4c2c4f2a
View on Chainz β†—

Height

#289,447

Difficulty

9.988532

Transactions

1

Size

207 B

Version

2

Bits

09fd1075

Nonce

214,943

Timestamp

12/2/2013, 5:13:52 AM

Confirmations

6,536,949

Merkle Root

c1bd3fe8c149882c1af9ee71d800bb7612a0b3e8b908cc4e7c81300be7d07ccc
Transactions (1)
Coinbasec1bd3fe8c14988…81300be7d07ccc
1 in β†’ 1 out10.0100 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.657 Γ— 10⁹⁢(97-digit number)
16577721598876554581…71696709109708848640
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
1.657 Γ— 10⁹⁢(97-digit number)
16577721598876554581…71696709109708848639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.657 Γ— 10⁹⁢(97-digit number)
16577721598876554581…71696709109708848641
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
3.315 Γ— 10⁹⁢(97-digit number)
33155443197753109163…43393418219417697279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.315 Γ— 10⁹⁢(97-digit number)
33155443197753109163…43393418219417697281
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
6.631 Γ— 10⁹⁢(97-digit number)
66310886395506218326…86786836438835394559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.631 Γ— 10⁹⁢(97-digit number)
66310886395506218326…86786836438835394561
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
1.326 Γ— 10⁹⁷(98-digit number)
13262177279101243665…73573672877670789119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.326 Γ— 10⁹⁷(98-digit number)
13262177279101243665…73573672877670789121
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
2.652 Γ— 10⁹⁷(98-digit number)
26524354558202487330…47147345755341578239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.652 Γ— 10⁹⁷(98-digit number)
26524354558202487330…47147345755341578241
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 289447

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 ca3364ebc84b7133ebeaa3334b397721a777636b6ae5459ff2a3ac0c4c2c4f2a

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 #289,447 on Chainz β†—
Circulating Supply:57,855,307 XPMΒ·at block #6,826,395 Β· updates every 60s
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