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Block #336,642

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/31/2013, 2:40:18 AM Β· Difficulty 10.1418 Β· 6,464,193 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7f03ac120c952e834abc2d10fdb5e79ef88d5eea47b10346b68fe4ea66f65e05
View on Chainz β†—

Height

#336,642

Difficulty

10.141763

Transactions

1

Size

210 B

Version

2

Bits

0a244a99

Nonce

21,226

Timestamp

12/31/2013, 2:40:18 AM

Confirmations

6,464,193

Merkle Root

b2c21e9a6e6f22b9c52247a3278f62a27461c045fa0507e0f86417002e5f5348
Transactions (1)
Coinbaseb2c21e9a6e6f22…6417002e5f5348
1 in β†’ 1 out9.7100 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.

1.628 Γ— 10¹⁰⁴(105-digit number)
16288969222363449658…93081124606611292160
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
1.628 Γ— 10¹⁰⁴(105-digit number)
16288969222363449658…93081124606611292159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.628 Γ— 10¹⁰⁴(105-digit number)
16288969222363449658…93081124606611292161
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
3.257 Γ— 10¹⁰⁴(105-digit number)
32577938444726899317…86162249213222584319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.257 Γ— 10¹⁰⁴(105-digit number)
32577938444726899317…86162249213222584321
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
6.515 Γ— 10¹⁰⁴(105-digit number)
65155876889453798634…72324498426445168639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.515 Γ— 10¹⁰⁴(105-digit number)
65155876889453798634…72324498426445168641
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
1.303 Γ— 10¹⁰⁡(106-digit number)
13031175377890759726…44648996852890337279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.303 Γ— 10¹⁰⁡(106-digit number)
13031175377890759726…44648996852890337281
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
2.606 Γ— 10¹⁰⁡(106-digit number)
26062350755781519453…89297993705780674559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.606 Γ— 10¹⁰⁡(106-digit number)
26062350755781519453…89297993705780674561
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 336642

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 7f03ac120c952e834abc2d10fdb5e79ef88d5eea47b10346b68fe4ea66f65e05

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 #336,642 on Chainz β†—
Circulating Supply:57,650,738 XPMΒ·at block #6,800,834 Β· updates every 60s
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