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Home/Chain Registry/Block #1,999,696

Block #1,999,696

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/26/2017, 4:55:59 AM Β· Difficulty 10.7409 Β· 4,825,877 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
104bb7e3715c1c2794b32eb9349c10fe55022b4e2afd18c2a8d8ccbe27ffcf41
View on Chainz β†—

Difficulty

10.740904

Transactions

1

Size

200 B

Version

2

Bits

0abdabe1

Nonce

1,587,588,952

Timestamp

2/26/2017, 4:55:59 AM

Confirmations

4,825,877

Merkle Root

58b2635cebc0a3b5a0c1e0b555f5d2c63d0474fdf841cef2e5888c49bad9e41a
Transactions (1)
Coinbase58b2635cebc0a3…888c49bad9e41a
1 in β†’ 1 out8.6500 XPM109 B
AWXR7qjJ…GPUbKBen
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.

3.370 Γ— 10⁹⁢(97-digit number)
33709252488786316871…86836048745050782720
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
3.370 Γ— 10⁹⁢(97-digit number)
33709252488786316871…86836048745050782719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.370 Γ— 10⁹⁢(97-digit number)
33709252488786316871…86836048745050782721
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
6.741 Γ— 10⁹⁢(97-digit number)
67418504977572633742…73672097490101565439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.741 Γ— 10⁹⁢(97-digit number)
67418504977572633742…73672097490101565441
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
1.348 Γ— 10⁹⁷(98-digit number)
13483700995514526748…47344194980203130879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.348 Γ— 10⁹⁷(98-digit number)
13483700995514526748…47344194980203130881
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
2.696 Γ— 10⁹⁷(98-digit number)
26967401991029053496…94688389960406261759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.696 Γ— 10⁹⁷(98-digit number)
26967401991029053496…94688389960406261761
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
5.393 Γ— 10⁹⁷(98-digit number)
53934803982058106993…89376779920812523519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.393 Γ— 10⁹⁷(98-digit number)
53934803982058106993…89376779920812523521
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
1.078 Γ— 10⁹⁸(99-digit number)
10786960796411621398…78753559841625047039
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 1999696

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 104bb7e3715c1c2794b32eb9349c10fe55022b4e2afd18c2a8d8ccbe27ffcf41

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 #1,999,696 on Chainz β†—
Circulating Supply:57,848,686 XPMΒ·at block #6,825,572 Β· updates every 60s
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