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Home/Chain Registry/Block #1,679,421

Block #1,679,421

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2016, 3:20:56 AM Β· Difficulty 10.7002 Β· 5,151,322 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2dd62b81d653dd256dbf512836b70b06629e4e3710cc9d0ef6d3eb925c828cc6
View on Chainz β†—

Difficulty

10.700201

Transactions

1

Size

201 B

Version

2

Bits

0ab34064

Nonce

1,489,669,688

Timestamp

7/19/2016, 3:20:56 AM

Confirmations

5,151,322

Merkle Root

9a0bbdee7f9b71cb0e662b4bd5ecf68a287357a0c5f04ec89839ccc86c4c14e6
Transactions (1)
Coinbase9a0bbdee7f9b71…39ccc86c4c14e6
1 in β†’ 1 out8.7200 XPM110 B
AMksKXSA…6Pd9buXQ
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.

1.462 Γ— 10⁹⁸(99-digit number)
14623628448878674446…35203476255590973440
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
1.462 Γ— 10⁹⁸(99-digit number)
14623628448878674446…35203476255590973439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.462 Γ— 10⁹⁸(99-digit number)
14623628448878674446…35203476255590973441
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
2.924 Γ— 10⁹⁸(99-digit number)
29247256897757348892…70406952511181946879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.924 Γ— 10⁹⁸(99-digit number)
29247256897757348892…70406952511181946881
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
5.849 Γ— 10⁹⁸(99-digit number)
58494513795514697784…40813905022363893759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.849 Γ— 10⁹⁸(99-digit number)
58494513795514697784…40813905022363893761
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
1.169 Γ— 10⁹⁹(100-digit number)
11698902759102939556…81627810044727787519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.169 Γ— 10⁹⁹(100-digit number)
11698902759102939556…81627810044727787521
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
2.339 Γ— 10⁹⁹(100-digit number)
23397805518205879113…63255620089455575039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.339 Γ— 10⁹⁹(100-digit number)
23397805518205879113…63255620089455575041
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 1679421

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 2dd62b81d653dd256dbf512836b70b06629e4e3710cc9d0ef6d3eb925c828cc6

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 #1,679,421 on Chainz β†—
Circulating Supply:57,890,082 XPMΒ·at block #6,830,742 Β· updates every 60s
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