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Home/Chain Registry/Block #2,642,677

Block #2,642,677

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 7:55:48 PM Β· Difficulty 11.6604 Β· 4,200,181 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
738fab9b39139d3d5c7115e5fde0b3cde2bbf751a19f4026fe040d07f73b4ff5
View on Chainz β†—

Difficulty

11.660415

Transactions

1

Size

199 B

Version

2

Bits

0ba910fd

Nonce

1,176,672,867

Timestamp

5/1/2018, 7:55:48 PM

Confirmations

4,200,181

Merkle Root

531dc78c6453ab2874428a76650c1ed03b76268016192f28c9582e8d7d484af6
Transactions (1)
Coinbase531dc78c6453ab…582e8d7d484af6
1 in β†’ 1 out7.3400 XPM110 B
ATnqpMia…k1c18kKw
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.

2.734 Γ— 10⁹³(94-digit number)
27345489773312621925…41588771115241954330
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
2.734 Γ— 10⁹³(94-digit number)
27345489773312621925…41588771115241954329
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.734 Γ— 10⁹³(94-digit number)
27345489773312621925…41588771115241954331
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
5.469 Γ— 10⁹³(94-digit number)
54690979546625243850…83177542230483908659
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.469 Γ— 10⁹³(94-digit number)
54690979546625243850…83177542230483908661
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
1.093 Γ— 10⁹⁴(95-digit number)
10938195909325048770…66355084460967817319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.093 Γ— 10⁹⁴(95-digit number)
10938195909325048770…66355084460967817321
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
2.187 Γ— 10⁹⁴(95-digit number)
21876391818650097540…32710168921935634639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.187 Γ— 10⁹⁴(95-digit number)
21876391818650097540…32710168921935634641
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
4.375 Γ— 10⁹⁴(95-digit number)
43752783637300195080…65420337843871269279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.375 Γ— 10⁹⁴(95-digit number)
43752783637300195080…65420337843871269281
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
8.750 Γ— 10⁹⁴(95-digit number)
87505567274600390160…30840675687742538559
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
8.750 Γ— 10⁹⁴(95-digit number)
87505567274600390160…30840675687742538561
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 2642677

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 738fab9b39139d3d5c7115e5fde0b3cde2bbf751a19f4026fe040d07f73b4ff5

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 #2,642,677 on Chainz β†—
Circulating Supply:57,987,211 XPMΒ·at block #6,842,857 Β· updates every 60s
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