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Block #855,242

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2014, 5:10:12 AM Β· Difficulty 10.9684 Β· 5,988,804 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4054e5faf682e562dfe55d5c82f23f6bdfa0caa690dc9b067f500e58ff2828ec
View on Chainz β†—

Height

#855,242

Difficulty

10.968433

Transactions

3

Size

626 B

Version

2

Bits

0af7eb37

Nonce

3,152,674,603

Timestamp

12/16/2014, 5:10:12 AM

Confirmations

5,988,804

Merkle Root

2770e02a1782fdbfc83b3ca8b5daf67193816d98199ef40d9a17e107308c15a1
Transactions (3)
Coinbaseb7681e7bccb47c…51efd4c31551d6
1 in β†’ 1 out8.3308 XPM116 B
ANSXnLY2…Sd25TjkD
10040c49e2ae3e…9f71b00a638169
1 in β†’ 2 out0.0397 XPM226 B
ALPB4NJc…hEZVrWhiAU9CNrB6…mwx2dbLr
27ba614fb7cb1e…fe175f331adeb8
1 in β†’ 1 out0.0119 XPM192 B
ALwSFQx6…eC5QGMwV
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.

2.108 Γ— 10⁹⁹(100-digit number)
21089413853345059760…34646178083548364800
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
2.108 Γ— 10⁹⁹(100-digit number)
21089413853345059760…34646178083548364799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.108 Γ— 10⁹⁹(100-digit number)
21089413853345059760…34646178083548364801
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
4.217 Γ— 10⁹⁹(100-digit number)
42178827706690119520…69292356167096729599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.217 Γ— 10⁹⁹(100-digit number)
42178827706690119520…69292356167096729601
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
8.435 Γ— 10⁹⁹(100-digit number)
84357655413380239041…38584712334193459199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.435 Γ— 10⁹⁹(100-digit number)
84357655413380239041…38584712334193459201
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
1.687 Γ— 10¹⁰⁰(101-digit number)
16871531082676047808…77169424668386918399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.687 Γ— 10¹⁰⁰(101-digit number)
16871531082676047808…77169424668386918401
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
3.374 Γ— 10¹⁰⁰(101-digit number)
33743062165352095616…54338849336773836799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.374 Γ— 10¹⁰⁰(101-digit number)
33743062165352095616…54338849336773836801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.748 Γ— 10¹⁰⁰(101-digit number)
67486124330704191232…08677698673547673599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 855242

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 4054e5faf682e562dfe55d5c82f23f6bdfa0caa690dc9b067f500e58ff2828ec

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 #855,242 on Chainz β†—
Circulating Supply:57,996,738 XPMΒ·at block #6,844,045 Β· updates every 60s
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