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Block #2,446,034

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/28/2017, 1:23:48 PM Β· Difficulty 10.9415 Β· 4,390,826 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
009b6e9f4e84d65003d11376e571da23e0abffeec7ea8b4c6a843461f547517b
View on Chainz β†—

Height

#2,446,034

Difficulty

10.941482

Transactions

1

Size

201 B

Version

2

Bits

0af104fb

Nonce

1,760,801,274

Timestamp

12/28/2017, 1:23:48 PM

Confirmations

4,390,826

Mined by

⛏️ P2SHAe9JVXEPZTtyBu9rGZCgwymwLVrV6WKL1U

Merkle Root

09f7d116ffd3ae24838dfafc9758ab86675477a99943f9eafef4c0b9e5630a44
Transactions (1)
Coinbase09f7d116ffd3ae…f4c0b9e5630a44
1 in β†’ 1 out8.3400 XPM110 B
Ae9JVXEP…rV6WKL1U
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.

7.938 Γ— 10⁹⁡(96-digit number)
79389584693062435424…73879310150022755839
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
7.938 Γ— 10⁹⁡(96-digit number)
79389584693062435424…73879310150022755839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.938 Γ— 10⁹⁡(96-digit number)
79389584693062435424…73879310150022755841
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
1.587 Γ— 10⁹⁢(97-digit number)
15877916938612487084…47758620300045511679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.587 Γ— 10⁹⁢(97-digit number)
15877916938612487084…47758620300045511681
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
3.175 Γ— 10⁹⁢(97-digit number)
31755833877224974169…95517240600091023359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.175 Γ— 10⁹⁢(97-digit number)
31755833877224974169…95517240600091023361
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
6.351 Γ— 10⁹⁢(97-digit number)
63511667754449948339…91034481200182046719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.351 Γ— 10⁹⁢(97-digit number)
63511667754449948339…91034481200182046721
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
1.270 Γ— 10⁹⁷(98-digit number)
12702333550889989667…82068962400364093439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.270 Γ— 10⁹⁷(98-digit number)
12702333550889989667…82068962400364093441
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
2.540 Γ— 10⁹⁷(98-digit number)
25404667101779979335…64137924800728186879
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.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,939,169 XPMΒ·at block #6,836,859 Β· updates every 60s
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