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Block #926,384

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/7/2015, 12:38:55 PM Β· Difficulty 10.9080 Β· 5,900,304 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1412adcb166d0323f87626188d6ba45daeb9707606f21e26e80c6f6cd36b6388
View on Chainz β†—

Height

#926,384

Difficulty

10.907951

Transactions

1

Size

207 B

Version

2

Bits

0ae86f75

Nonce

1,508,759,303

Timestamp

2/7/2015, 12:38:55 PM

Confirmations

5,900,304

Merkle Root

317659dc2b1346f5b4c833a956f515610fe81d77ce51f58715e93f80ac5a60ac
Transactions (1)
Coinbase317659dc2b1346…e93f80ac5a60ac
1 in β†’ 1 out8.3900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

8.554 Γ— 10⁹⁡(96-digit number)
85540651199252619519…60187024008420061440
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
8.554 Γ— 10⁹⁡(96-digit number)
85540651199252619519…60187024008420061439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.554 Γ— 10⁹⁡(96-digit number)
85540651199252619519…60187024008420061441
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
1.710 Γ— 10⁹⁢(97-digit number)
17108130239850523903…20374048016840122879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.710 Γ— 10⁹⁢(97-digit number)
17108130239850523903…20374048016840122881
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
3.421 Γ— 10⁹⁢(97-digit number)
34216260479701047807…40748096033680245759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.421 Γ— 10⁹⁢(97-digit number)
34216260479701047807…40748096033680245761
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
6.843 Γ— 10⁹⁢(97-digit number)
68432520959402095615…81496192067360491519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.843 Γ— 10⁹⁢(97-digit number)
68432520959402095615…81496192067360491521
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
1.368 Γ— 10⁹⁷(98-digit number)
13686504191880419123…62992384134720983039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.368 Γ— 10⁹⁷(98-digit number)
13686504191880419123…62992384134720983041
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 926384

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 1412adcb166d0323f87626188d6ba45daeb9707606f21e26e80c6f6cd36b6388

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 #926,384 on Chainz β†—
Circulating Supply:57,857,654 XPMΒ·at block #6,826,687 Β· updates every 60s
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