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Home/Chain Registry/Block #1,688,253

Block #1,688,253

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2016, 3:59:04 AM Β· Difficulty 10.7096 Β· 5,148,171 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e41494ba78ed4b76be46b6e69371d954b773db38bd81a870eca3aa050e20a3e2
View on Chainz β†—

Difficulty

10.709584

Transactions

1

Size

200 B

Version

2

Bits

0ab5a746

Nonce

1,521,591,097

Timestamp

7/25/2016, 3:59:04 AM

Confirmations

5,148,171

Merkle Root

b7b9976a5cfefe1fb08f95ee7663ffda058fb592b27d9b50bf6cc434a48321d8
Transactions (1)
Coinbaseb7b9976a5cfefe…6cc434a48321d8
1 in β†’ 1 out8.7100 XPM110 B
AN5v5GRP…8CaoZ37J
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.

3.436 Γ— 10⁹⁴(95-digit number)
34366486842182733471…77037512411852350200
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
3.436 Γ— 10⁹⁴(95-digit number)
34366486842182733471…77037512411852350199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.436 Γ— 10⁹⁴(95-digit number)
34366486842182733471…77037512411852350201
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
6.873 Γ— 10⁹⁴(95-digit number)
68732973684365466943…54075024823704700399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.873 Γ— 10⁹⁴(95-digit number)
68732973684365466943…54075024823704700401
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
1.374 Γ— 10⁹⁡(96-digit number)
13746594736873093388…08150049647409400799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.374 Γ— 10⁹⁡(96-digit number)
13746594736873093388…08150049647409400801
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
2.749 Γ— 10⁹⁡(96-digit number)
27493189473746186777…16300099294818801599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.749 Γ— 10⁹⁡(96-digit number)
27493189473746186777…16300099294818801601
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
5.498 Γ— 10⁹⁡(96-digit number)
54986378947492373554…32600198589637603199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.498 Γ— 10⁹⁡(96-digit number)
54986378947492373554…32600198589637603201
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 1688253

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 e41494ba78ed4b76be46b6e69371d954b773db38bd81a870eca3aa050e20a3e2

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 #1,688,253 on Chainz β†—
Circulating Supply:57,935,659 XPMΒ·at block #6,836,423 Β· updates every 60s
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