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Block #226,958

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/25/2013, 2:08:03 PM Β· Difficulty 9.9360 Β· 6,614,631 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6837537a29cddcca0b18e76bc54ac1f174e6f1412c4fdaaa03e75ff285eeca06
View on Chainz β†—

Height

#226,958

Difficulty

9.936039

Transactions

1

Size

207 B

Version

2

Bits

09efa048

Nonce

525

Timestamp

10/25/2013, 2:08:03 PM

Confirmations

6,614,631

Merkle Root

9f243b8b852d14adab2a22103974404993d439809998a96ec6300ebf3d16f7b8
Transactions (1)
Coinbase9f243b8b852d14…300ebf3d16f7b8
1 in β†’ 1 out10.1100 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.

4.563 Γ— 10⁹⁢(97-digit number)
45635527268323880231…64750752341095404800
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
4.563 Γ— 10⁹⁢(97-digit number)
45635527268323880231…64750752341095404799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.563 Γ— 10⁹⁢(97-digit number)
45635527268323880231…64750752341095404801
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
9.127 Γ— 10⁹⁢(97-digit number)
91271054536647760462…29501504682190809599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.127 Γ— 10⁹⁢(97-digit number)
91271054536647760462…29501504682190809601
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
1.825 Γ— 10⁹⁷(98-digit number)
18254210907329552092…59003009364381619199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.825 Γ— 10⁹⁷(98-digit number)
18254210907329552092…59003009364381619201
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
3.650 Γ— 10⁹⁷(98-digit number)
36508421814659104185…18006018728763238399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.650 Γ— 10⁹⁷(98-digit number)
36508421814659104185…18006018728763238401
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
7.301 Γ— 10⁹⁷(98-digit number)
73016843629318208370…36012037457526476799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 226958

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 6837537a29cddcca0b18e76bc54ac1f174e6f1412c4fdaaa03e75ff285eeca06

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 #226,958 on Chainz β†—
Circulating Supply:57,977,099 XPMΒ·at block #6,841,588 Β· updates every 60s
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