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Home/Chain Registry/Block #2,635,330

Block #2,635,330

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 5:20:17 AM Β· Difficulty 11.3071 Β· 4,201,124 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c56788ecaf37852220003d27ce87264bc5316817978f42e1436dd6e6c016b466
View on Chainz β†—

Difficulty

11.307094

Transactions

1

Size

200 B

Version

2

Bits

0b4e9db3

Nonce

7,293,164

Timestamp

4/29/2018, 5:20:17 AM

Confirmations

4,201,124

Merkle Root

43d9ab16b75b51d6af43937b7434c1a0690fb348b83a92de41968e2f66ce9d4f
Transactions (1)
Coinbase43d9ab16b75b51…968e2f66ce9d4f
1 in β†’ 1 out7.8100 XPM110 B
Adqah8zh…1WwoHJ9t
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.

4.798 Γ— 10⁹³(94-digit number)
47983735898441221595…37468781435664672720
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
4.798 Γ— 10⁹³(94-digit number)
47983735898441221595…37468781435664672719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.798 Γ— 10⁹³(94-digit number)
47983735898441221595…37468781435664672721
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
9.596 Γ— 10⁹³(94-digit number)
95967471796882443190…74937562871329345439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.596 Γ— 10⁹³(94-digit number)
95967471796882443190…74937562871329345441
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
1.919 Γ— 10⁹⁴(95-digit number)
19193494359376488638…49875125742658690879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.919 Γ— 10⁹⁴(95-digit number)
19193494359376488638…49875125742658690881
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
3.838 Γ— 10⁹⁴(95-digit number)
38386988718752977276…99750251485317381759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.838 Γ— 10⁹⁴(95-digit number)
38386988718752977276…99750251485317381761
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
7.677 Γ— 10⁹⁴(95-digit number)
76773977437505954552…99500502970634763519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.677 Γ— 10⁹⁴(95-digit number)
76773977437505954552…99500502970634763521
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
1.535 Γ— 10⁹⁡(96-digit number)
15354795487501190910…99001005941269527039
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 2635330

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 c56788ecaf37852220003d27ce87264bc5316817978f42e1436dd6e6c016b466

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 #2,635,330 on Chainz β†—
Circulating Supply:57,935,903 XPMΒ·at block #6,836,453 Β· updates every 60s
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