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Block #352,847

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2014, 2:37:12 PM Β· Difficulty 10.3123 Β· 6,463,226 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
42bb8e260e1f30c8ca4e7731f8a459749fb41e0494ecf9b3c086bb71f10f0691
View on Chainz β†—

Height

#352,847

Difficulty

10.312341

Transactions

1

Size

210 B

Version

2

Bits

0a4ff59a

Nonce

11,577

Timestamp

1/10/2014, 2:37:12 PM

Confirmations

6,463,226

Merkle Root

f24d1c7c8293d10188bc83af034f842f99453f82254ea8507c0979540947540f
Transactions (1)
Coinbasef24d1c7c8293d1…0979540947540f
1 in β†’ 1 out9.3900 XPM116 B
AbwWkWZt…kawDhufa
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.

1.133 Γ— 10¹⁰⁡(106-digit number)
11336445038772799507…92710683364694118280
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
1.133 Γ— 10¹⁰⁡(106-digit number)
11336445038772799507…92710683364694118279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.133 Γ— 10¹⁰⁡(106-digit number)
11336445038772799507…92710683364694118281
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
2.267 Γ— 10¹⁰⁡(106-digit number)
22672890077545599015…85421366729388236559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.267 Γ— 10¹⁰⁡(106-digit number)
22672890077545599015…85421366729388236561
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
4.534 Γ— 10¹⁰⁡(106-digit number)
45345780155091198031…70842733458776473119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.534 Γ— 10¹⁰⁡(106-digit number)
45345780155091198031…70842733458776473121
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
9.069 Γ— 10¹⁰⁡(106-digit number)
90691560310182396063…41685466917552946239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.069 Γ— 10¹⁰⁡(106-digit number)
90691560310182396063…41685466917552946241
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
1.813 Γ— 10¹⁰⁢(107-digit number)
18138312062036479212…83370933835105892479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.813 Γ— 10¹⁰⁢(107-digit number)
18138312062036479212…83370933835105892481
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 352847

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 42bb8e260e1f30c8ca4e7731f8a459749fb41e0494ecf9b3c086bb71f10f0691

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 #352,847 on Chainz β†—
Circulating Supply:57,772,701 XPMΒ·at block #6,816,072 Β· updates every 60s
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