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Block #264,962

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/19/2013, 3:51:08 AM Β· Difficulty 9.9634 Β· 6,561,193 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
70a2c6d6afb7be220b57a196732e191b85a3198d6221a6c3b1e5166d7399e2aa
View on Chainz β†—

Height

#264,962

Difficulty

9.963446

Transactions

1

Size

231 B

Version

2

Bits

09f6a469

Nonce

9,495

Timestamp

11/19/2013, 3:51:08 AM

Confirmations

6,561,193

Merkle Root

14d1cae5721f47b3a6c8f740681a3c38f266b824f717376bc00b31c344b4998e
Transactions (1)
Coinbase14d1cae5721f47…0b31c344b4998e
1 in β†’ 2 out10.0600 XPM141 B
AdGRRh1e…QmctLb24AHsw4d6U…EnM8UXNZ
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.

7.866 Γ— 10⁹⁴(95-digit number)
78667783227916337805…89670134213250523480
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
7.866 Γ— 10⁹⁴(95-digit number)
78667783227916337805…89670134213250523479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.866 Γ— 10⁹⁴(95-digit number)
78667783227916337805…89670134213250523481
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
1.573 Γ— 10⁹⁡(96-digit number)
15733556645583267561…79340268426501046959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.573 Γ— 10⁹⁡(96-digit number)
15733556645583267561…79340268426501046961
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
3.146 Γ— 10⁹⁡(96-digit number)
31467113291166535122…58680536853002093919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.146 Γ— 10⁹⁡(96-digit number)
31467113291166535122…58680536853002093921
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
6.293 Γ— 10⁹⁡(96-digit number)
62934226582333070244…17361073706004187839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.293 Γ— 10⁹⁡(96-digit number)
62934226582333070244…17361073706004187841
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
1.258 Γ— 10⁹⁢(97-digit number)
12586845316466614048…34722147412008375679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.258 Γ— 10⁹⁢(97-digit number)
12586845316466614048…34722147412008375681
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 264962

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 70a2c6d6afb7be220b57a196732e191b85a3198d6221a6c3b1e5166d7399e2aa

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 #264,962 on Chainz β†—
Circulating Supply:57,853,366 XPMΒ·at block #6,826,154 Β· updates every 60s
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