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Home/Chain Registry/Block #2,635,326

Block #2,635,326

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 5:17:11 AM Β· Difficulty 11.3070 Β· 4,195,419 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b0e2b7279a98e62557a3d69075c29e67e7758889ceacfb39b323c4f88c4cddb5
View on Chainz β†—

Difficulty

11.306958

Transactions

1

Size

200 B

Version

2

Bits

0b4e94d4

Nonce

938,349,004

Timestamp

4/29/2018, 5:17:11 AM

Confirmations

4,195,419

Merkle Root

1a645385c6ff32415c1d628400330070b2bdad56d5dcbc84db31fd69ecceecc0
Transactions (1)
Coinbase1a645385c6ff32…31fd69ecceecc0
1 in β†’ 1 out7.8100 XPM110 B
ALWfKFcn…bvdBRJEZ
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.

6.861 Γ— 10⁹⁡(96-digit number)
68615536084520155570…54081699452176564480
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
6.861 Γ— 10⁹⁡(96-digit number)
68615536084520155570…54081699452176564479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.861 Γ— 10⁹⁡(96-digit number)
68615536084520155570…54081699452176564481
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
1.372 Γ— 10⁹⁢(97-digit number)
13723107216904031114…08163398904353128959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.372 Γ— 10⁹⁢(97-digit number)
13723107216904031114…08163398904353128961
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
2.744 Γ— 10⁹⁢(97-digit number)
27446214433808062228…16326797808706257919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.744 Γ— 10⁹⁢(97-digit number)
27446214433808062228…16326797808706257921
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
5.489 Γ— 10⁹⁢(97-digit number)
54892428867616124456…32653595617412515839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.489 Γ— 10⁹⁢(97-digit number)
54892428867616124456…32653595617412515841
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
1.097 Γ— 10⁹⁷(98-digit number)
10978485773523224891…65307191234825031679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.097 Γ— 10⁹⁷(98-digit number)
10978485773523224891…65307191234825031681
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
2.195 Γ— 10⁹⁷(98-digit number)
21956971547046449782…30614382469650063359
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 2635326

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 b0e2b7279a98e62557a3d69075c29e67e7758889ceacfb39b323c4f88c4cddb5

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 #2,635,326 on Chainz β†—
Circulating Supply:57,890,096 XPMΒ·at block #6,830,744 Β· updates every 60s
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