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Home/Chain Registry/Block #1,166,413

Block #1,166,413

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/23/2015, 6:36:10 AM Β· Difficulty 10.9341 Β· 5,679,240 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2701b96522828c509614987293aa810caf9879282b250b14ebf5e47ef629ff90
View on Chainz β†—

Difficulty

10.934060

Transactions

1

Size

199 B

Version

2

Bits

0aef1e91

Nonce

460,744,361

Timestamp

7/23/2015, 6:36:10 AM

Confirmations

5,679,240

Merkle Root

a5d0d4e87ca7b594190191b82565b810eb613718502385af0e931534b84387e4
Transactions (1)
Coinbasea5d0d4e87ca7b5…931534b84387e4
1 in β†’ 1 out8.3500 XPM109 B
AZJggPNe…kzRrXown
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.

1.196 Γ— 10⁹⁡(96-digit number)
11960771943052883739…03184763169398205760
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
1.196 Γ— 10⁹⁡(96-digit number)
11960771943052883739…03184763169398205759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.196 Γ— 10⁹⁡(96-digit number)
11960771943052883739…03184763169398205761
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
2.392 Γ— 10⁹⁡(96-digit number)
23921543886105767478…06369526338796411519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.392 Γ— 10⁹⁡(96-digit number)
23921543886105767478…06369526338796411521
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
4.784 Γ— 10⁹⁡(96-digit number)
47843087772211534956…12739052677592823039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.784 Γ— 10⁹⁡(96-digit number)
47843087772211534956…12739052677592823041
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
9.568 Γ— 10⁹⁡(96-digit number)
95686175544423069913…25478105355185646079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.568 Γ— 10⁹⁡(96-digit number)
95686175544423069913…25478105355185646081
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
1.913 Γ— 10⁹⁢(97-digit number)
19137235108884613982…50956210710371292159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.913 Γ— 10⁹⁢(97-digit number)
19137235108884613982…50956210710371292161
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 1166413

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 2701b96522828c509614987293aa810caf9879282b250b14ebf5e47ef629ff90

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 #1,166,413 on Chainz β†—
Circulating Supply:58,009,672 XPMΒ·at block #6,845,652 Β· updates every 60s
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