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Block #2,822,909

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/3/2018, 1:58:21 PM Β· Difficulty 11.7036 Β· 4,022,332 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eac8dbb7ac98d77018c4b36e8ad275af7b044105e15093794a5df679172acd22
View on Chainz β†—

Height

#2,822,909

Difficulty

11.703582

Transactions

1

Size

201 B

Version

2

Bits

0bb41df1

Nonce

1,447,583,301

Timestamp

9/3/2018, 1:58:21 PM

Confirmations

4,022,332

Mined by

⛏️ P2SHAcJoDFTFEDCmPaTRdSPGXYoo4GhZGXNRJt

Merkle Root

d10afb880cf41bf39aeefb5bdf566e3ec834927e9f968c512d05ca18054ea319
Transactions (1)
Coinbased10afb880cf41b…05ca18054ea319
1 in β†’ 1 out7.2900 XPM109 B
AcJoDFTF…hZGXNRJt
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.

3.585 Γ— 10⁹⁸(99-digit number)
35858569737634511251…48941395780180275199
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
3.585 Γ— 10⁹⁸(99-digit number)
35858569737634511251…48941395780180275199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.585 Γ— 10⁹⁸(99-digit number)
35858569737634511251…48941395780180275201
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
7.171 Γ— 10⁹⁸(99-digit number)
71717139475269022502…97882791560360550399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.171 Γ— 10⁹⁸(99-digit number)
71717139475269022502…97882791560360550401
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
1.434 Γ— 10⁹⁹(100-digit number)
14343427895053804500…95765583120721100799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.434 Γ— 10⁹⁹(100-digit number)
14343427895053804500…95765583120721100801
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
2.868 Γ— 10⁹⁹(100-digit number)
28686855790107609000…91531166241442201599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.868 Γ— 10⁹⁹(100-digit number)
28686855790107609000…91531166241442201601
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
5.737 Γ— 10⁹⁹(100-digit number)
57373711580215218001…83062332482884403199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.737 Γ— 10⁹⁹(100-digit number)
57373711580215218001…83062332482884403201
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
1.147 Γ— 10¹⁰⁰(101-digit number)
11474742316043043600…66124664965768806399
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:58,006,360 XPMΒ·at block #6,845,240 Β· updates every 60s
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