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Block #258,065

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/12/2013, 8:08:22 PM Β· Difficulty 9.9762 Β· 6,542,515 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
59da99c63eed4577cb3a311e4c52b3164ad97dbf3502f3a4da649bc4ad9be124
View on Chainz β†—

Height

#258,065

Difficulty

9.976200

Transactions

2

Size

606 B

Version

2

Bits

09f9e840

Nonce

6,575

Timestamp

11/12/2013, 8:08:22 PM

Confirmations

6,542,515

Merkle Root

64fe176baddfd29d3caeb4294ea7607c12b351c86f6df2b544bd92456aa50154
Transactions (2)
Coinbase8ad57341f52295…0c9cfac69b5255
1 in β†’ 2 out10.0400 XPM141 B
AdGRRh1e…QmctLb24ASNt3cJa…L5zCqAYM
f3810a12f31936…65f9e00b2a4316
2 in β†’ 2 out32.8440 XPM374 B
AUC766Yj…kTCsi6qyATjLuGyA…b2LyEFzM
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.

2.278 Γ— 10⁹⁢(97-digit number)
22784844509490633601…11416035148683752360
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
2.278 Γ— 10⁹⁢(97-digit number)
22784844509490633601…11416035148683752359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.278 Γ— 10⁹⁢(97-digit number)
22784844509490633601…11416035148683752361
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
4.556 Γ— 10⁹⁢(97-digit number)
45569689018981267203…22832070297367504719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.556 Γ— 10⁹⁢(97-digit number)
45569689018981267203…22832070297367504721
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
9.113 Γ— 10⁹⁢(97-digit number)
91139378037962534407…45664140594735009439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.113 Γ— 10⁹⁢(97-digit number)
91139378037962534407…45664140594735009441
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
1.822 Γ— 10⁹⁷(98-digit number)
18227875607592506881…91328281189470018879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.822 Γ— 10⁹⁷(98-digit number)
18227875607592506881…91328281189470018881
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
3.645 Γ— 10⁹⁷(98-digit number)
36455751215185013762…82656562378940037759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.645 Γ— 10⁹⁷(98-digit number)
36455751215185013762…82656562378940037761
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 258065

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 59da99c63eed4577cb3a311e4c52b3164ad97dbf3502f3a4da649bc4ad9be124

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 #258,065 on Chainz β†—
Circulating Supply:57,648,697 XPMΒ·at block #6,800,579 Β· updates every 60s
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