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Block #2,641,852

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 12:26:37 PM Β· Difficulty 11.6341 Β· 4,189,506 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
96b64ccbb3b0b3819deac6e8326c17a36441acb335a8250d79e712a902eb70cf
View on Chainz β†—

Difficulty

11.634059

Transactions

1

Size

201 B

Version

2

Bits

0ba251b0

Nonce

414,997,436

Timestamp

5/1/2018, 12:26:37 PM

Confirmations

4,189,506

Merkle Root

ff06bd514f1c136fe22722ec60b0f040191633e51c4538a5c73f263ea34d44a2
Transactions (1)
Coinbaseff06bd514f1c13…3f263ea34d44a2
1 in β†’ 1 out7.3800 XPM110 B
ASeDV9Se…svum17GB
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.

1.319 Γ— 10⁹⁢(97-digit number)
13198695069830203958…96918250233285335040
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
1.319 Γ— 10⁹⁢(97-digit number)
13198695069830203958…96918250233285335039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.319 Γ— 10⁹⁢(97-digit number)
13198695069830203958…96918250233285335041
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
2.639 Γ— 10⁹⁢(97-digit number)
26397390139660407917…93836500466570670079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.639 Γ— 10⁹⁢(97-digit number)
26397390139660407917…93836500466570670081
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
5.279 Γ— 10⁹⁢(97-digit number)
52794780279320815835…87673000933141340159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.279 Γ— 10⁹⁢(97-digit number)
52794780279320815835…87673000933141340161
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
1.055 Γ— 10⁹⁷(98-digit number)
10558956055864163167…75346001866282680319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.055 Γ— 10⁹⁷(98-digit number)
10558956055864163167…75346001866282680321
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
2.111 Γ— 10⁹⁷(98-digit number)
21117912111728326334…50692003732565360639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.111 Γ— 10⁹⁷(98-digit number)
21117912111728326334…50692003732565360641
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
4.223 Γ— 10⁹⁷(98-digit number)
42235824223456652668…01384007465130721279
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 2641852

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 96b64ccbb3b0b3819deac6e8326c17a36441acb335a8250d79e712a902eb70cf

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 #2,641,852 on Chainz β†—
Circulating Supply:57,895,018 XPMΒ·at block #6,831,357 Β· updates every 60s
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