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Home/Chain Registry/Block #1,726,038

Block #1,726,038

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/20/2016, 1:13:12 PM Β· Difficulty 10.6986 Β· 5,082,305 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca128c4b6f2e55ae2c8311fbd66d78a0f60b9795fa0ba7648de6544469ca4e44
View on Chainz β†—

Difficulty

10.698560

Transactions

1

Size

199 B

Version

2

Bits

0ab2d4d6

Nonce

1,460,538,810

Timestamp

8/20/2016, 1:13:12 PM

Confirmations

5,082,305

Merkle Root

ba6e16c562138023ec51c57fed6353de303212d67d8b4fa050fb473a3403702b
Transactions (1)
Coinbaseba6e16c5621380…fb473a3403702b
1 in β†’ 1 out8.7200 XPM109 B
AR7SJTnr…yN8sM9W2
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.

1.723 Γ— 10⁹⁡(96-digit number)
17235100559403726471…51061353226319599200
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
1.723 Γ— 10⁹⁡(96-digit number)
17235100559403726471…51061353226319599199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.723 Γ— 10⁹⁡(96-digit number)
17235100559403726471…51061353226319599201
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
3.447 Γ— 10⁹⁡(96-digit number)
34470201118807452942…02122706452639198399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.447 Γ— 10⁹⁡(96-digit number)
34470201118807452942…02122706452639198401
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
6.894 Γ— 10⁹⁡(96-digit number)
68940402237614905884…04245412905278396799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.894 Γ— 10⁹⁡(96-digit number)
68940402237614905884…04245412905278396801
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
1.378 Γ— 10⁹⁢(97-digit number)
13788080447522981176…08490825810556793599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.378 Γ— 10⁹⁢(97-digit number)
13788080447522981176…08490825810556793601
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
2.757 Γ— 10⁹⁢(97-digit number)
27576160895045962353…16981651621113587199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.757 Γ— 10⁹⁢(97-digit number)
27576160895045962353…16981651621113587201
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 1726038

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 ca128c4b6f2e55ae2c8311fbd66d78a0f60b9795fa0ba7648de6544469ca4e44

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 #1,726,038 on Chainz β†—
Circulating Supply:57,710,801 XPMΒ·at block #6,808,342 Β· updates every 60s
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