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Block #196,024

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/6/2013, 5:29:23 AM Β· Difficulty 9.8802 Β· 6,628,859 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1f33307b1ee36fa86f35b071a0b7e945a67e5bac7ba4ea0da843ef7fcd768171
View on Chainz β†—

Height

#196,024

Difficulty

9.880213

Transactions

1

Size

199 B

Version

2

Bits

09e155a8

Nonce

10,597

Timestamp

10/6/2013, 5:29:23 AM

Confirmations

6,628,859

Merkle Root

68799c592ddb2bcc41103e63bd43002dc81db0492f23a9d0f8ebcc284eebe6ef
Transactions (1)
Coinbase68799c592ddb2b…ebcc284eebe6ef
1 in β†’ 1 out10.2300 XPM110 B
ANvtpRa1…QjsraDJz
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.

3.465 Γ— 10⁹²(93-digit number)
34657242394184895919…46239538981790729000
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
3.465 Γ— 10⁹²(93-digit number)
34657242394184895919…46239538981790728999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.465 Γ— 10⁹²(93-digit number)
34657242394184895919…46239538981790729001
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
6.931 Γ— 10⁹²(93-digit number)
69314484788369791839…92479077963581457999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.931 Γ— 10⁹²(93-digit number)
69314484788369791839…92479077963581458001
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
1.386 Γ— 10⁹³(94-digit number)
13862896957673958367…84958155927162915999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.386 Γ— 10⁹³(94-digit number)
13862896957673958367…84958155927162916001
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
2.772 Γ— 10⁹³(94-digit number)
27725793915347916735…69916311854325831999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.772 Γ— 10⁹³(94-digit number)
27725793915347916735…69916311854325832001
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
5.545 Γ— 10⁹³(94-digit number)
55451587830695833471…39832623708651663999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.545 Γ— 10⁹³(94-digit number)
55451587830695833471…39832623708651664001
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 196024

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 1f33307b1ee36fa86f35b071a0b7e945a67e5bac7ba4ea0da843ef7fcd768171

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 #196,024 on Chainz β†—
Circulating Supply:57,843,146 XPMΒ·at block #6,824,882 Β· updates every 60s
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