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Home/Chain Registry/Block #1,658,291

Block #1,658,291

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/3/2016, 3:16:18 AM Β· Difficulty 10.7943 Β· 5,183,043 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d5e2aebbb7e71716f0ef1e98a05a157fca8e002ed42f7613c30a8c8d973d681
View on Chainz β†—

Difficulty

10.794275

Transactions

1

Size

242 B

Version

2

Bits

0acb559a

Nonce

1,368,205,803

Timestamp

7/3/2016, 3:16:18 AM

Confirmations

5,183,043

Merkle Root

bc58073be5f018187541f68326ddba2d7561db431a36cf4a55224abacd23a9b3
Transactions (1)
Coinbasebc58073be5f018…224abacd23a9b3
1 in β†’ 2 out8.5700 XPM152 B
AJgZBh3x…9DpUcwi5ALPu3s2c…EJXLjVFh
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.

2.921 Γ— 10⁹⁡(96-digit number)
29219552572208047357…88302134868908033190
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
2.921 Γ— 10⁹⁡(96-digit number)
29219552572208047357…88302134868908033189
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.921 Γ— 10⁹⁡(96-digit number)
29219552572208047357…88302134868908033191
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
5.843 Γ— 10⁹⁡(96-digit number)
58439105144416094714…76604269737816066379
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.843 Γ— 10⁹⁡(96-digit number)
58439105144416094714…76604269737816066381
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
1.168 Γ— 10⁹⁢(97-digit number)
11687821028883218942…53208539475632132759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.168 Γ— 10⁹⁢(97-digit number)
11687821028883218942…53208539475632132761
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
2.337 Γ— 10⁹⁢(97-digit number)
23375642057766437885…06417078951264265519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.337 Γ— 10⁹⁢(97-digit number)
23375642057766437885…06417078951264265521
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
4.675 Γ— 10⁹⁢(97-digit number)
46751284115532875771…12834157902528531039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.675 Γ— 10⁹⁢(97-digit number)
46751284115532875771…12834157902528531041
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 1658291

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 4d5e2aebbb7e71716f0ef1e98a05a157fca8e002ed42f7613c30a8c8d973d681

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 #1,658,291 on Chainz β†—
Circulating Supply:57,975,036 XPMΒ·at block #6,841,333 Β· updates every 60s
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