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Home/Chain Registry/Block #2,634,302

Block #2,634,302

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 8:17:18 PM Β· Difficulty 11.2371 Β· 4,198,125 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
65c2c527f10f88fee6dbec3ac0d6dab2ce190eec1be950fc9e4026db42d51007
View on Chainz β†—

Difficulty

11.237095

Transactions

2

Size

572 B

Version

2

Bits

0b3cb245

Nonce

1,047,875,046

Timestamp

4/28/2018, 8:17:18 PM

Confirmations

4,198,125

Merkle Root

bd3789295a6aae4308c56932e6daa44004bb80c297c36d48cedbdab02f57bc57
Transactions (2)
Coinbasec41af104beed6c…3db1c0bcd96a62
1 in β†’ 1 out7.9200 XPM110 B
Adqah8zh…1WwoHJ9t
1cb3058876ca9d…725d11da15aa99
2 in β†’ 2 out349.7670 XPM373 B
Ae2ict5s…rbHdwtwNAJHHtshE…jc4mKjCY
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.

2.629 Γ— 10⁹³(94-digit number)
26299326811477163637…17505262561815904600
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
2.629 Γ— 10⁹³(94-digit number)
26299326811477163637…17505262561815904599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.629 Γ— 10⁹³(94-digit number)
26299326811477163637…17505262561815904601
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
5.259 Γ— 10⁹³(94-digit number)
52598653622954327275…35010525123631809199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.259 Γ— 10⁹³(94-digit number)
52598653622954327275…35010525123631809201
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
1.051 Γ— 10⁹⁴(95-digit number)
10519730724590865455…70021050247263618399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.051 Γ— 10⁹⁴(95-digit number)
10519730724590865455…70021050247263618401
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
2.103 Γ— 10⁹⁴(95-digit number)
21039461449181730910…40042100494527236799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.103 Γ— 10⁹⁴(95-digit number)
21039461449181730910…40042100494527236801
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
4.207 Γ— 10⁹⁴(95-digit number)
42078922898363461820…80084200989054473599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.207 Γ— 10⁹⁴(95-digit number)
42078922898363461820…80084200989054473601
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
8.415 Γ— 10⁹⁴(95-digit number)
84157845796726923641…60168401978108947199
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 2634302

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 65c2c527f10f88fee6dbec3ac0d6dab2ce190eec1be950fc9e4026db42d51007

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 #2,634,302 on Chainz β†—
Circulating Supply:57,903,562 XPMΒ·at block #6,832,426 Β· updates every 60s
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