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Block #318,217

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/18/2013, 5:18:08 AM Β· Difficulty 10.1588 Β· 6,481,997 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3da39b4e82d2317bb743510caaf3711f066ae3ccfbf177f6940027eabcb3f652
View on Chainz β†—

Height

#318,217

Difficulty

10.158764

Transactions

3

Size

766 B

Version

2

Bits

0a28a4ba

Nonce

676

Timestamp

12/18/2013, 5:18:08 AM

Confirmations

6,481,997

Merkle Root

ebf65b34380c2fb1bea49893883f08d544a6be5c605fc75d447883ce8d43c2fa
Transactions (3)
Coinbaseb657afd714c7df…51da3104fc0443
1 in β†’ 1 out9.7000 XPM109 B
AWT4FajA…7qUxCsaJ
b8968cfe276af0…e02c7cae225c25
1 in β†’ 1 out3.0430 XPM191 B
AePUc49t…4zC5VvXd
7bfe91be950c2d…37f0e1d6d6588a
2 in β†’ 2 out1.1271 XPM376 B
AHKRLU1g…gVTAoWoxAGB3HZRH…7ZkMh8ic
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.

1.956 Γ— 10⁹⁡(96-digit number)
19565077653701895485…85732727306956177300
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
1.956 Γ— 10⁹⁡(96-digit number)
19565077653701895485…85732727306956177299
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.956 Γ— 10⁹⁡(96-digit number)
19565077653701895485…85732727306956177301
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
3.913 Γ— 10⁹⁡(96-digit number)
39130155307403790970…71465454613912354599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.913 Γ— 10⁹⁡(96-digit number)
39130155307403790970…71465454613912354601
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
7.826 Γ— 10⁹⁡(96-digit number)
78260310614807581941…42930909227824709199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.826 Γ— 10⁹⁡(96-digit number)
78260310614807581941…42930909227824709201
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
1.565 Γ— 10⁹⁢(97-digit number)
15652062122961516388…85861818455649418399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.565 Γ— 10⁹⁢(97-digit number)
15652062122961516388…85861818455649418401
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
3.130 Γ— 10⁹⁢(97-digit number)
31304124245923032776…71723636911298836799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.130 Γ— 10⁹⁢(97-digit number)
31304124245923032776…71723636911298836801
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 318217

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 3da39b4e82d2317bb743510caaf3711f066ae3ccfbf177f6940027eabcb3f652

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 #318,217 on Chainz β†—
Circulating Supply:57,645,762 XPMΒ·at block #6,800,213 Β· updates every 60s
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