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Block #2,934,521

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/22/2018, 3:17:07 PM Β· Difficulty 11.3930 Β· 3,903,891 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5dcc23154018f999747f865988f81be3866917444836b8a4a5db949d48e3eca0
View on Chainz β†—

Height

#2,934,521

Difficulty

11.392956

Transactions

1

Size

201 B

Version

2

Bits

0b6498c6

Nonce

1,170,867,015

Timestamp

11/22/2018, 3:17:07 PM

Confirmations

3,903,891

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

26fb5c118fcc3cef31ba320eccc444663d10186948f8b07af59fcf1029678d5d
Transactions (1)
Coinbase26fb5c118fcc3c…9fcf1029678d5d
1 in β†’ 1 out7.6900 XPM110 B
AbXwmGxD…4XXYP765
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.

1.134 Γ— 10⁹⁸(99-digit number)
11347368652529653128…75604877100472319999
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
1.134 Γ— 10⁹⁸(99-digit number)
11347368652529653128…75604877100472319999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.134 Γ— 10⁹⁸(99-digit number)
11347368652529653128…75604877100472320001
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
2.269 Γ— 10⁹⁸(99-digit number)
22694737305059306257…51209754200944639999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.269 Γ— 10⁹⁸(99-digit number)
22694737305059306257…51209754200944640001
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
4.538 Γ— 10⁹⁸(99-digit number)
45389474610118612515…02419508401889279999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.538 Γ— 10⁹⁸(99-digit number)
45389474610118612515…02419508401889280001
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
9.077 Γ— 10⁹⁸(99-digit number)
90778949220237225031…04839016803778559999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.077 Γ— 10⁹⁸(99-digit number)
90778949220237225031…04839016803778560001
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
1.815 Γ— 10⁹⁹(100-digit number)
18155789844047445006…09678033607557119999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.815 Γ— 10⁹⁹(100-digit number)
18155789844047445006…09678033607557120001
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
3.631 Γ— 10⁹⁹(100-digit number)
36311579688094890012…19356067215114239999
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:57,951,569 XPMΒ·at block #6,838,411 Β· updates every 60s
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