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Home/Chain Registry/Block #3,364,738

Block #3,364,738

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/22/2019, 7:57:22 AM Β· Difficulty 10.9954 Β· 3,466,187 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
50edd843acd5b3e90e5e44f4adc854c71fe87ac24110d22e4f944abd430af1f8
View on Chainz β†—

Difficulty

10.995448

Transactions

1

Size

202 B

Version

2

Bits

0afed5af

Nonce

1,104,239,769

Timestamp

9/22/2019, 7:57:22 AM

Confirmations

3,466,187

Merkle Root

db66bcf09bd99dad183bf880f986f85c1f5d73b6d83785635538ed87ef7f0cf0
Transactions (1)
Coinbasedb66bcf09bd99d…38ed87ef7f0cf0
1 in β†’ 1 out8.2600 XPM110 B
Aa32y8PQ…e3Enbehj
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.

4.585 Γ— 10⁹⁸(99-digit number)
45857401510344715989…40165609323089428480
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
4.585 Γ— 10⁹⁸(99-digit number)
45857401510344715989…40165609323089428479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.585 Γ— 10⁹⁸(99-digit number)
45857401510344715989…40165609323089428481
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
9.171 Γ— 10⁹⁸(99-digit number)
91714803020689431979…80331218646178856959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.171 Γ— 10⁹⁸(99-digit number)
91714803020689431979…80331218646178856961
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
1.834 Γ— 10⁹⁹(100-digit number)
18342960604137886395…60662437292357713919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.834 Γ— 10⁹⁹(100-digit number)
18342960604137886395…60662437292357713921
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
3.668 Γ— 10⁹⁹(100-digit number)
36685921208275772791…21324874584715427839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.668 Γ— 10⁹⁹(100-digit number)
36685921208275772791…21324874584715427841
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
7.337 Γ— 10⁹⁹(100-digit number)
73371842416551545583…42649749169430855679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.337 Γ— 10⁹⁹(100-digit number)
73371842416551545583…42649749169430855681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.467 Γ— 10¹⁰⁰(101-digit number)
14674368483310309116…85299498338861711359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 3364738

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 50edd843acd5b3e90e5e44f4adc854c71fe87ac24110d22e4f944abd430af1f8

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 #3,364,738 on Chainz β†—
Circulating Supply:57,891,531 XPMΒ·at block #6,830,924 Β· updates every 60s
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