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Block #164,345

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2013, 2:55:32 PM Β· Difficulty 9.8623 Β· 6,631,023 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
37cebc044ef8fa9e41b0afc43f59a03406a3395326e0aeaa4c5cf007f6a65840
View on Chainz β†—

Height

#164,345

Difficulty

9.862253

Transactions

1

Size

202 B

Version

2

Bits

09dcbc9a

Nonce

16,781,406

Timestamp

9/14/2013, 2:55:32 PM

Confirmations

6,631,023

Merkle Root

77317909c0e58bc1d307ea19fc0eb8c3a9c65ead3a33ba2c9b716f650899f987
Transactions (1)
Coinbase77317909c0e58b…716f650899f987
1 in β†’ 1 out10.2700 XPM112 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.

5.203 Γ— 10⁹⁴(95-digit number)
52037264101331520635…86644037441370831680
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
5.203 Γ— 10⁹⁴(95-digit number)
52037264101331520635…86644037441370831679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.203 Γ— 10⁹⁴(95-digit number)
52037264101331520635…86644037441370831681
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
1.040 Γ— 10⁹⁡(96-digit number)
10407452820266304127…73288074882741663359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.040 Γ— 10⁹⁡(96-digit number)
10407452820266304127…73288074882741663361
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
2.081 Γ— 10⁹⁡(96-digit number)
20814905640532608254…46576149765483326719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.081 Γ— 10⁹⁡(96-digit number)
20814905640532608254…46576149765483326721
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
4.162 Γ— 10⁹⁡(96-digit number)
41629811281065216508…93152299530966653439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.162 Γ— 10⁹⁡(96-digit number)
41629811281065216508…93152299530966653441
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
8.325 Γ— 10⁹⁡(96-digit number)
83259622562130433016…86304599061933306879
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 164345

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 37cebc044ef8fa9e41b0afc43f59a03406a3395326e0aeaa4c5cf007f6a65840

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 #164,345 on Chainz β†—
Circulating Supply:57,607,000 XPMΒ·at block #6,795,367 Β· updates every 60s
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