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Home/Chain Registry/Block #1,639,083

Block #1,639,083

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2016, 12:54:54 AM Β· Difficulty 10.7061 Β· 5,162,127 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
58d67b1be80f81dff87c112dad2c7a9e021d2c7e97c1422b44b78a619f41f323
View on Chainz β†—

Difficulty

10.706126

Transactions

1

Size

201 B

Version

2

Bits

0ab4c4b2

Nonce

1,702,080,758

Timestamp

6/21/2016, 12:54:54 AM

Confirmations

5,162,127

Merkle Root

98e56a428cf8fb2a16737138a8caafa95b3df4839f6d755a379884e40ab36127
Transactions (1)
Coinbase98e56a428cf8fb…9884e40ab36127
1 in β†’ 1 out8.7100 XPM110 B
AVVmm3oo…7HWQogKT
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.

1.190 Γ— 10⁹⁸(99-digit number)
11900058271746633475…77019650331642880000
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
1.190 Γ— 10⁹⁸(99-digit number)
11900058271746633475…77019650331642879999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.190 Γ— 10⁹⁸(99-digit number)
11900058271746633475…77019650331642880001
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
2.380 Γ— 10⁹⁸(99-digit number)
23800116543493266951…54039300663285759999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.380 Γ— 10⁹⁸(99-digit number)
23800116543493266951…54039300663285760001
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
4.760 Γ— 10⁹⁸(99-digit number)
47600233086986533902…08078601326571519999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.760 Γ— 10⁹⁸(99-digit number)
47600233086986533902…08078601326571520001
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
9.520 Γ— 10⁹⁸(99-digit number)
95200466173973067805…16157202653143039999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.520 Γ— 10⁹⁸(99-digit number)
95200466173973067805…16157202653143040001
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
1.904 Γ— 10⁹⁹(100-digit number)
19040093234794613561…32314405306286079999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.904 Γ— 10⁹⁹(100-digit number)
19040093234794613561…32314405306286080001
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
3.808 Γ— 10⁹⁹(100-digit number)
38080186469589227122…64628810612572159999
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 1639083

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 58d67b1be80f81dff87c112dad2c7a9e021d2c7e97c1422b44b78a619f41f323

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 #1,639,083 on Chainz β†—
Circulating Supply:57,653,745 XPMΒ·at block #6,801,209 Β· updates every 60s
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