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Home/Chain Registry/Block #2,169,704

Block #2,169,704

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2017, 2:06:25 AM Β· Difficulty 10.9004 Β· 4,674,753 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3a4e0e5b5bed2525c617fd1648d3f9a3aa502c0851549340f876ae1657a06b6e
View on Chainz β†—

Difficulty

10.900370

Transactions

1

Size

201 B

Version

2

Bits

0ae67ea0

Nonce

359,590,397

Timestamp

6/21/2017, 2:06:25 AM

Confirmations

4,674,753

Merkle Root

c5a32dbd8197f25e1f57f1674b4a0c46c2f38e73d7a2444bdab8a2c67c20bd08
Transactions (1)
Coinbasec5a32dbd8197f2…b8a2c67c20bd08
1 in β†’ 1 out8.4000 XPM110 B
AFwwrEVm…y92ab1Uq
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.

1.137 Γ— 10⁹⁢(97-digit number)
11373330215809266767…04638542022848757760
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
1.137 Γ— 10⁹⁢(97-digit number)
11373330215809266767…04638542022848757759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.137 Γ— 10⁹⁢(97-digit number)
11373330215809266767…04638542022848757761
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
2.274 Γ— 10⁹⁢(97-digit number)
22746660431618533534…09277084045697515519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.274 Γ— 10⁹⁢(97-digit number)
22746660431618533534…09277084045697515521
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
4.549 Γ— 10⁹⁢(97-digit number)
45493320863237067069…18554168091395031039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.549 Γ— 10⁹⁢(97-digit number)
45493320863237067069…18554168091395031041
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
9.098 Γ— 10⁹⁢(97-digit number)
90986641726474134139…37108336182790062079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.098 Γ— 10⁹⁢(97-digit number)
90986641726474134139…37108336182790062081
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
1.819 Γ— 10⁹⁷(98-digit number)
18197328345294826827…74216672365580124159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.819 Γ— 10⁹⁷(98-digit number)
18197328345294826827…74216672365580124161
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 2169704

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 3a4e0e5b5bed2525c617fd1648d3f9a3aa502c0851549340f876ae1657a06b6e

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 #2,169,704 on Chainz β†—
Circulating Supply:58,000,055 XPMΒ·at block #6,844,456 Β· updates every 60s
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