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Block #842,993

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/7/2014, 1:47:14 AM Β· Difficulty 10.9733 Β· 5,996,252 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5131f6f12d12d2b8223b856d4c0f736f09ef78256ff35116e69fbaa4e246e114
View on Chainz β†—

Height

#842,993

Difficulty

10.973311

Transactions

2

Size

433 B

Version

2

Bits

0af92aeb

Nonce

379,750,945

Timestamp

12/7/2014, 1:47:14 AM

Confirmations

5,996,252

Merkle Root

3c376b4682136da1764017c452b886145d2ad777887ba2f307dcc27af1235f89
Transactions (2)
Coinbase5fc4a92e6bfc9b…24cb908e62a2df
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
529aa0b08b087b…6b554029b33271
1 in β†’ 2 out0.1527 XPM226 B
Adyw59Pg…eAfAJrQdANANmnT2…HTXAFxLb
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.

5.428 Γ— 10⁹⁷(98-digit number)
54285921424156497080…76093998004054261760
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
5.428 Γ— 10⁹⁷(98-digit number)
54285921424156497080…76093998004054261759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.428 Γ— 10⁹⁷(98-digit number)
54285921424156497080…76093998004054261761
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
1.085 Γ— 10⁹⁸(99-digit number)
10857184284831299416…52187996008108523519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.085 Γ— 10⁹⁸(99-digit number)
10857184284831299416…52187996008108523521
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
2.171 Γ— 10⁹⁸(99-digit number)
21714368569662598832…04375992016217047039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.171 Γ— 10⁹⁸(99-digit number)
21714368569662598832…04375992016217047041
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
4.342 Γ— 10⁹⁸(99-digit number)
43428737139325197664…08751984032434094079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.342 Γ— 10⁹⁸(99-digit number)
43428737139325197664…08751984032434094081
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
8.685 Γ— 10⁹⁸(99-digit number)
86857474278650395329…17503968064868188159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.685 Γ— 10⁹⁸(99-digit number)
86857474278650395329…17503968064868188161
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
1.737 Γ— 10⁹⁹(100-digit number)
17371494855730079065…35007936129736376319
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 842993

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 5131f6f12d12d2b8223b856d4c0f736f09ef78256ff35116e69fbaa4e246e114

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 #842,993 on Chainz β†—
Circulating Supply:57,958,243 XPMΒ·at block #6,839,244 Β· updates every 60s
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