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Home/Chain Registry/Block #2,103,699

Block #2,103,699

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/6/2017, 10:35:32 PM Β· Difficulty 10.8761 Β· 4,729,703 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7dc7daa333c73c817aa1485c49f6a25ed77b51ba1e4530fc31ec3f7e2fc37b8f
View on Chainz β†—

Difficulty

10.876131

Transactions

1

Size

199 B

Version

2

Bits

0ae04a19

Nonce

380,678,005

Timestamp

5/6/2017, 10:35:32 PM

Confirmations

4,729,703

Merkle Root

329b8eed66927bc8deffcbc226124f20e7d689a96d5f74b3bd07a9a049064723
Transactions (1)
Coinbase329b8eed66927b…07a9a049064723
1 in β†’ 1 out8.4400 XPM109 B
AcYd4JFv…NSzNQAY1
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.

2.549 Γ— 10⁹³(94-digit number)
25494088799181699011…51499010253136856000
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
2.549 Γ— 10⁹³(94-digit number)
25494088799181699011…51499010253136855999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.549 Γ— 10⁹³(94-digit number)
25494088799181699011…51499010253136856001
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
5.098 Γ— 10⁹³(94-digit number)
50988177598363398023…02998020506273711999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.098 Γ— 10⁹³(94-digit number)
50988177598363398023…02998020506273712001
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
1.019 Γ— 10⁹⁴(95-digit number)
10197635519672679604…05996041012547423999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.019 Γ— 10⁹⁴(95-digit number)
10197635519672679604…05996041012547424001
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
2.039 Γ— 10⁹⁴(95-digit number)
20395271039345359209…11992082025094847999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.039 Γ— 10⁹⁴(95-digit number)
20395271039345359209…11992082025094848001
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
4.079 Γ— 10⁹⁴(95-digit number)
40790542078690718418…23984164050189695999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.079 Γ— 10⁹⁴(95-digit number)
40790542078690718418…23984164050189696001
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 2103699

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 7dc7daa333c73c817aa1485c49f6a25ed77b51ba1e4530fc31ec3f7e2fc37b8f

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 #2,103,699 on Chainz β†—
Circulating Supply:57,911,416 XPMΒ·at block #6,833,401 Β· updates every 60s
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