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Block #2,634,254

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 7:55:49 PM Β· Difficulty 11.2330 Β· 4,196,615 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6e27b35ec317188ac754f1e4a65b892f847628ab20066dceeaeced5e2968a5e8
View on Chainz β†—

Height

#2,634,254

Difficulty

11.233041

Transactions

2

Size

1.49 KB

Version

2

Bits

0b3ba89b

Nonce

459,149,838

Timestamp

4/28/2018, 7:55:49 PM

Confirmations

4,196,615

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

74afc3d2829a4f00256e501aeeb8ae7d550c52dcd684ef7bf09644c3ab1cb12c
Transactions (2)
Coinbase4e167aee168982…5969796ff83a0f
1 in β†’ 1 out7.9300 XPM110 B
Adqah8zh…1WwoHJ9t
34a265222dc19b…60e2aa6073185f
8 in β†’ 4 out39.4376 XPM1.30 KB
ARznVePF…S7wvbB9sAXeumsZ2…t3Hx1fGZAPi8C85f…Lg5MDieiASk9H3sY…qUG8r1d4
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.

4.626 Γ— 10⁹⁷(98-digit number)
46265189256365291343…88519262740052095999
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
4.626 Γ— 10⁹⁷(98-digit number)
46265189256365291343…88519262740052095999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.626 Γ— 10⁹⁷(98-digit number)
46265189256365291343…88519262740052096001
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
9.253 Γ— 10⁹⁷(98-digit number)
92530378512730582686…77038525480104191999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.253 Γ— 10⁹⁷(98-digit number)
92530378512730582686…77038525480104192001
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
1.850 Γ— 10⁹⁸(99-digit number)
18506075702546116537…54077050960208383999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.850 Γ— 10⁹⁸(99-digit number)
18506075702546116537…54077050960208384001
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
3.701 Γ— 10⁹⁸(99-digit number)
37012151405092233074…08154101920416767999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.701 Γ— 10⁹⁸(99-digit number)
37012151405092233074…08154101920416768001
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
7.402 Γ— 10⁹⁸(99-digit number)
74024302810184466149…16308203840833535999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.402 Γ— 10⁹⁸(99-digit number)
74024302810184466149…16308203840833536001
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
1.480 Γ— 10⁹⁹(100-digit number)
14804860562036893229…32616407681667071999
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:57,891,090 XPMΒ·at block #6,830,868 Β· updates every 60s
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