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Block #2,611,565

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/13/2018, 3:42:59 AM Β· Difficulty 11.2143 Β· 4,229,064 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d5b240ff7e4f175aed66f071bb5bedabdb228a858e3143b40ac75bc5884ac204
View on Chainz β†—

Difficulty

11.214254

Transactions

1

Size

199 B

Version

2

Bits

0b36d959

Nonce

71,892,498

Timestamp

4/13/2018, 3:42:59 AM

Confirmations

4,229,064

Merkle Root

be7cdedf999f80c64904eaaee1c2bd1b45d04e15dc2a0df8153d9d4c845edfc8
Transactions (1)
Coinbasebe7cdedf999f80…3d9d4c845edfc8
1 in β†’ 1 out7.9400 XPM110 B
Adqah8zh…1WwoHJ9t
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.

9.535 Γ— 10⁹²(93-digit number)
95351387787634779136…61444809022220235520
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
9.535 Γ— 10⁹²(93-digit number)
95351387787634779136…61444809022220235519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.535 Γ— 10⁹²(93-digit number)
95351387787634779136…61444809022220235521
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
1.907 Γ— 10⁹³(94-digit number)
19070277557526955827…22889618044440471039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.907 Γ— 10⁹³(94-digit number)
19070277557526955827…22889618044440471041
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
3.814 Γ— 10⁹³(94-digit number)
38140555115053911654…45779236088880942079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.814 Γ— 10⁹³(94-digit number)
38140555115053911654…45779236088880942081
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
7.628 Γ— 10⁹³(94-digit number)
76281110230107823309…91558472177761884159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.628 Γ— 10⁹³(94-digit number)
76281110230107823309…91558472177761884161
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
1.525 Γ— 10⁹⁴(95-digit number)
15256222046021564661…83116944355523768319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.525 Γ— 10⁹⁴(95-digit number)
15256222046021564661…83116944355523768321
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
3.051 Γ— 10⁹⁴(95-digit number)
30512444092043129323…66233888711047536639
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 2611565

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 d5b240ff7e4f175aed66f071bb5bedabdb228a858e3143b40ac75bc5884ac204

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 #2,611,565 on Chainz β†—
Circulating Supply:57,969,372 XPMΒ·at block #6,840,628 Β· updates every 60s
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