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Block #2,650,365

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2018, 11:57:36 PM Β· Difficulty 11.7572 Β· 4,191,423 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e9ac422e13cf979d9d859228c978f3a5e4bbc23c2733f79c1f3ce818819331e5
View on Chainz β†—

Height

#2,650,365

Difficulty

11.757186

Transactions

1

Size

202 B

Version

2

Bits

0bc1d6ef

Nonce

1,033,484,201

Timestamp

5/5/2018, 11:57:36 PM

Confirmations

4,191,423

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

9209109cb1b7136afd7e64e21a89011e65173f38e3d0893145f98bcf2d5d3076
Transactions (1)
Coinbase9209109cb1b713…f98bcf2d5d3076
1 in β†’ 1 out7.2200 XPM110 B
Adqah8zh…1WwoHJ9t
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.

3.152 Γ— 10⁹⁸(99-digit number)
31525630744224517694…35580768858085785599
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
3.152 Γ— 10⁹⁸(99-digit number)
31525630744224517694…35580768858085785599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.152 Γ— 10⁹⁸(99-digit number)
31525630744224517694…35580768858085785601
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
6.305 Γ— 10⁹⁸(99-digit number)
63051261488449035389…71161537716171571199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.305 Γ— 10⁹⁸(99-digit number)
63051261488449035389…71161537716171571201
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
1.261 Γ— 10⁹⁹(100-digit number)
12610252297689807077…42323075432343142399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.261 Γ— 10⁹⁹(100-digit number)
12610252297689807077…42323075432343142401
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
2.522 Γ— 10⁹⁹(100-digit number)
25220504595379614155…84646150864686284799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.522 Γ— 10⁹⁹(100-digit number)
25220504595379614155…84646150864686284801
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
5.044 Γ— 10⁹⁹(100-digit number)
50441009190759228311…69292301729372569599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.044 Γ— 10⁹⁹(100-digit number)
50441009190759228311…69292301729372569601
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
1.008 Γ— 10¹⁰⁰(101-digit number)
10088201838151845662…38584603458745139199
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:57,978,682 XPMΒ·at block #6,841,787 Β· updates every 60s
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