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Block #206,924

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/13/2013, 3:06:52 AM Β· Difficulty 9.9017 Β· 6,619,599 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
54880ff25f56d05187dc8606126bc51d681e6c6bc9a69fedf131760f39f0cebd
View on Chainz β†—

Height

#206,924

Difficulty

9.901735

Transactions

1

Size

205 B

Version

2

Bits

09e6d821

Nonce

134,221,059

Timestamp

10/13/2013, 3:06:52 AM

Confirmations

6,619,599

Merkle Root

7300aaa02a5a3fe6722852b7e62f0bb98a384e81a313ae7440f0d3930e08d981
Transactions (1)
Coinbase7300aaa02a5a3f…f0d3930e08d981
1 in β†’ 1 out10.1800 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.286 Γ— 10⁹²(93-digit number)
12868193817397001954…09824460123211050240
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
1.286 Γ— 10⁹²(93-digit number)
12868193817397001954…09824460123211050239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.286 Γ— 10⁹²(93-digit number)
12868193817397001954…09824460123211050241
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
2.573 Γ— 10⁹²(93-digit number)
25736387634794003909…19648920246422100479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.573 Γ— 10⁹²(93-digit number)
25736387634794003909…19648920246422100481
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
5.147 Γ— 10⁹²(93-digit number)
51472775269588007819…39297840492844200959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.147 Γ— 10⁹²(93-digit number)
51472775269588007819…39297840492844200961
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
1.029 Γ— 10⁹³(94-digit number)
10294555053917601563…78595680985688401919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.029 Γ— 10⁹³(94-digit number)
10294555053917601563…78595680985688401921
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
2.058 Γ— 10⁹³(94-digit number)
20589110107835203127…57191361971376803839
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 206924

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 54880ff25f56d05187dc8606126bc51d681e6c6bc9a69fedf131760f39f0cebd

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 #206,924 on Chainz β†—
Circulating Supply:57,856,329 XPMΒ·at block #6,826,522 Β· updates every 60s
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