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Home/Chain Registry/Block #2,936,113

Block #2,936,113

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/23/2018, 6:22:24 PM Β· Difficulty 11.3890 Β· 3,897,804 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
68efbff1aff7ac19a37a276d1e9c97584336249cf1ce5937616ed43ca30994e8
View on Chainz β†—

Difficulty

11.389039

Transactions

1

Size

202 B

Version

2

Bits

0b639817

Nonce

1,406,447,723

Timestamp

11/23/2018, 6:22:24 PM

Confirmations

3,897,804

Merkle Root

3a2e72857e2d67830d59220d27d9a5913eb9ef5c885429941cd92d82d4b68cb2
Transactions (1)
Coinbase3a2e72857e2d67…d92d82d4b68cb2
1 in β†’ 1 out7.7000 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.438 Γ— 10⁹⁹(100-digit number)
14386755593758820818…88008622622075125760
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
1.438 Γ— 10⁹⁹(100-digit number)
14386755593758820818…88008622622075125759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.438 Γ— 10⁹⁹(100-digit number)
14386755593758820818…88008622622075125761
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
2.877 Γ— 10⁹⁹(100-digit number)
28773511187517641636…76017245244150251519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.877 Γ— 10⁹⁹(100-digit number)
28773511187517641636…76017245244150251521
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
5.754 Γ— 10⁹⁹(100-digit number)
57547022375035283272…52034490488300503039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.754 Γ— 10⁹⁹(100-digit number)
57547022375035283272…52034490488300503041
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
1.150 Γ— 10¹⁰⁰(101-digit number)
11509404475007056654…04068980976601006079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.150 Γ— 10¹⁰⁰(101-digit number)
11509404475007056654…04068980976601006081
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
2.301 Γ— 10¹⁰⁰(101-digit number)
23018808950014113308…08137961953202012159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.301 Γ— 10¹⁰⁰(101-digit number)
23018808950014113308…08137961953202012161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.603 Γ— 10¹⁰⁰(101-digit number)
46037617900028226617…16275923906404024319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2936113

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 68efbff1aff7ac19a37a276d1e9c97584336249cf1ce5937616ed43ca30994e8

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 #2,936,113 on Chainz β†—
Circulating Supply:57,915,562 XPMΒ·at block #6,833,916 Β· updates every 60s
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