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Home/Chain Registry/Block #2,634,036

Block #2,634,036

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 5:46:33 PM Β· Difficulty 11.2194 Β· 4,206,454 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca1a748e5ab8660226d9c9a5d8d89384edbda3315bb423603d7a9b9b84668127
View on Chainz β†—

Difficulty

11.219423

Transactions

1

Size

201 B

Version

2

Bits

0b382c18

Nonce

366,103,356

Timestamp

4/28/2018, 5:46:33 PM

Confirmations

4,206,454

Merkle Root

305f2a6e10ecffbdfd5b8b99919ab0c94050dabfa146a57e6e837ea1d7bc4708
Transactions (1)
Coinbase305f2a6e10ecff…837ea1d7bc4708
1 in β†’ 1 out7.9300 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.

9.662 Γ— 10⁹⁡(96-digit number)
96629631019324250078…81786673407591710720
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
9.662 Γ— 10⁹⁡(96-digit number)
96629631019324250078…81786673407591710719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.662 Γ— 10⁹⁡(96-digit number)
96629631019324250078…81786673407591710721
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
1.932 Γ— 10⁹⁢(97-digit number)
19325926203864850015…63573346815183421439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.932 Γ— 10⁹⁢(97-digit number)
19325926203864850015…63573346815183421441
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
3.865 Γ— 10⁹⁢(97-digit number)
38651852407729700031…27146693630366842879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.865 Γ— 10⁹⁢(97-digit number)
38651852407729700031…27146693630366842881
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
7.730 Γ— 10⁹⁢(97-digit number)
77303704815459400063…54293387260733685759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.730 Γ— 10⁹⁢(97-digit number)
77303704815459400063…54293387260733685761
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
1.546 Γ— 10⁹⁷(98-digit number)
15460740963091880012…08586774521467371519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.546 Γ— 10⁹⁷(98-digit number)
15460740963091880012…08586774521467371521
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
3.092 Γ— 10⁹⁷(98-digit number)
30921481926183760025…17173549042934743039
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 2634036

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 ca1a748e5ab8660226d9c9a5d8d89384edbda3315bb423603d7a9b9b84668127

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 #2,634,036 on Chainz β†—
Circulating Supply:57,968,252 XPMΒ·at block #6,840,489 Β· updates every 60s
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