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Home/Chain Registry/Block #2,634,297

Block #2,634,297

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 8:15:28 PM Β· Difficulty 11.2368 Β· 4,208,706 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27f992a43bfab5feba328c58cbce8e4b4cfd4848fc1e73cf2ab0d83a7d0f25e6
View on Chainz β†—

Difficulty

11.236817

Transactions

2

Size

725 B

Version

2

Bits

0b3ca011

Nonce

298,624,369

Timestamp

4/28/2018, 8:15:28 PM

Confirmations

4,208,706

Merkle Root

c32cafdf08c0f224d405907c2cb52d2fd7c0291e6af0e49a180134610e6a6d30
Transactions (2)
Coinbasee234fd8eab6fa7…a375f0cf1426ea
1 in β†’ 1 out7.9200 XPM110 B
Adqah8zh…1WwoHJ9t
5a0307844d7521…065f57d4ce574e
3 in β†’ 2 out363.3895 XPM524 B
ARTGxeAc…WmRAvHDaASbnn2Vs…1eCmu1FY
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.

1.917 Γ— 10⁹⁷(98-digit number)
19174421738023888881…14627799399267368960
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
1.917 Γ— 10⁹⁷(98-digit number)
19174421738023888881…14627799399267368959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.917 Γ— 10⁹⁷(98-digit number)
19174421738023888881…14627799399267368961
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
3.834 Γ— 10⁹⁷(98-digit number)
38348843476047777763…29255598798534737919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.834 Γ— 10⁹⁷(98-digit number)
38348843476047777763…29255598798534737921
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
7.669 Γ— 10⁹⁷(98-digit number)
76697686952095555527…58511197597069475839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.669 Γ— 10⁹⁷(98-digit number)
76697686952095555527…58511197597069475841
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
1.533 Γ— 10⁹⁸(99-digit number)
15339537390419111105…17022395194138951679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.533 Γ— 10⁹⁸(99-digit number)
15339537390419111105…17022395194138951681
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
3.067 Γ— 10⁹⁸(99-digit number)
30679074780838222211…34044790388277903359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.067 Γ— 10⁹⁸(99-digit number)
30679074780838222211…34044790388277903361
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
6.135 Γ— 10⁹⁸(99-digit number)
61358149561676444422…68089580776555806719
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
6.135 Γ— 10⁹⁸(99-digit number)
61358149561676444422…68089580776555806721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2634297

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 27f992a43bfab5feba328c58cbce8e4b4cfd4848fc1e73cf2ab0d83a7d0f25e6

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 #2,634,297 on Chainz β†—
Circulating Supply:57,988,380 XPMΒ·at block #6,843,002 Β· updates every 60s
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