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Home/Chain Registry/Block #2,634,071

Block #2,634,071

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 6:10:11 PM Β· Difficulty 11.2213 Β· 4,207,855 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c089e6c7c97085ec9d2e33f282372c9967d82670eb87c5d031464fbada5d0fce
View on Chainz β†—

Difficulty

11.221329

Transactions

1

Size

200 B

Version

2

Bits

0b38a907

Nonce

8,779,788

Timestamp

4/28/2018, 6:10:11 PM

Confirmations

4,207,855

Merkle Root

ae91280c6d97fb72eb7530e3cc06d22f53037b5982853a355d92633c9a57e1e5
Transactions (1)
Coinbaseae91280c6d97fb…92633c9a57e1e5
1 in β†’ 1 out7.9300 XPM110 B
ASwxAK86…xRUtQ9gM
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.

2.263 Γ— 10⁹³(94-digit number)
22637104884514872946…68098908950790864000
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
2.263 Γ— 10⁹³(94-digit number)
22637104884514872946…68098908950790863999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.263 Γ— 10⁹³(94-digit number)
22637104884514872946…68098908950790864001
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
4.527 Γ— 10⁹³(94-digit number)
45274209769029745893…36197817901581727999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.527 Γ— 10⁹³(94-digit number)
45274209769029745893…36197817901581728001
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
9.054 Γ— 10⁹³(94-digit number)
90548419538059491786…72395635803163455999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.054 Γ— 10⁹³(94-digit number)
90548419538059491786…72395635803163456001
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
1.810 Γ— 10⁹⁴(95-digit number)
18109683907611898357…44791271606326911999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.810 Γ— 10⁹⁴(95-digit number)
18109683907611898357…44791271606326912001
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
3.621 Γ— 10⁹⁴(95-digit number)
36219367815223796714…89582543212653823999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.621 Γ— 10⁹⁴(95-digit number)
36219367815223796714…89582543212653824001
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
7.243 Γ— 10⁹⁴(95-digit number)
72438735630447593429…79165086425307647999
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 2634071

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 c089e6c7c97085ec9d2e33f282372c9967d82670eb87c5d031464fbada5d0fce

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 #2,634,071 on Chainz β†—
Circulating Supply:57,979,785 XPMΒ·at block #6,841,925 Β· updates every 60s
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