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Block #271,759

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/24/2013, 7:54:38 PM Β· Difficulty 9.9524 Β· 6,542,318 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dee62d2677837c537f8d8c7299b7b929a223268be765a33b433b687a304388fd
View on Chainz β†—

Height

#271,759

Difficulty

9.952357

Transactions

2

Size

1020 B

Version

2

Bits

09f3cda3

Nonce

27,648

Timestamp

11/24/2013, 7:54:38 PM

Confirmations

6,542,318

Merkle Root

939aa92e3cdda8ceeaf5ffcba41c741974c23ea278c3486588f92cff63293994
Transactions (2)
Coinbase79a8f1c3d0276f…b290929ff2ca14
1 in β†’ 1 out10.0900 XPM109 B
AMa2WoKe…RgX4EdWb
ad86f5c76774fe…59e9cd3bc0b962
5 in β†’ 2 out657.5919 XPM820 B
AUAcH6kx…3NAWZoVRAV1XaCWZ…2ZTgHVdW
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.

8.501 Γ— 10⁹⁡(96-digit number)
85016819258141434043…96616863942469588800
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
8.501 Γ— 10⁹⁡(96-digit number)
85016819258141434043…96616863942469588799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.501 Γ— 10⁹⁡(96-digit number)
85016819258141434043…96616863942469588801
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
1.700 Γ— 10⁹⁢(97-digit number)
17003363851628286808…93233727884939177599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.700 Γ— 10⁹⁢(97-digit number)
17003363851628286808…93233727884939177601
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
3.400 Γ— 10⁹⁢(97-digit number)
34006727703256573617…86467455769878355199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.400 Γ— 10⁹⁢(97-digit number)
34006727703256573617…86467455769878355201
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
6.801 Γ— 10⁹⁢(97-digit number)
68013455406513147234…72934911539756710399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.801 Γ— 10⁹⁢(97-digit number)
68013455406513147234…72934911539756710401
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
1.360 Γ— 10⁹⁷(98-digit number)
13602691081302629446…45869823079513420799
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 271759

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 dee62d2677837c537f8d8c7299b7b929a223268be765a33b433b687a304388fd

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 #271,759 on Chainz β†—
Circulating Supply:57,756,696 XPMΒ·at block #6,814,076 Β· updates every 60s
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