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Block #2,580,268

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/23/2018, 3:05:19 AM Β· Difficulty 11.0365 Β· 4,256,085 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f5e8d76a3428b8ca5a3d07dda908422edc470c9d8cb068a8eba05f2bef51f5b0
View on Chainz β†—

Height

#2,580,268

Difficulty

11.036518

Transactions

2

Size

8.07 KB

Version

2

Bits

0b095938

Nonce

625,735,070

Timestamp

3/23/2018, 3:05:19 AM

Confirmations

4,256,085

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

c8bd47bca996267222ac89c177ccdf11affa549fd290ab9bfde050449ce629b9
Transactions (2)
Coinbase44d3a66136824f…f9953c8575877b
1 in β†’ 1 out8.2900 XPM109 B
Adqah8zh…1WwoHJ9t
979138471374ea…72bc7a8b547c8a
54 in β†’ 2 out271.4739 XPM7.88 KB
AS7LRS8s…iaW2W6juAKGxoSP8…8oH3hVLd
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.

1.803 Γ— 10⁹⁡(96-digit number)
18039627750751502365…47861854878773958399
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
1.803 Γ— 10⁹⁡(96-digit number)
18039627750751502365…47861854878773958399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.803 Γ— 10⁹⁡(96-digit number)
18039627750751502365…47861854878773958401
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
3.607 Γ— 10⁹⁡(96-digit number)
36079255501503004731…95723709757547916799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.607 Γ— 10⁹⁡(96-digit number)
36079255501503004731…95723709757547916801
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
7.215 Γ— 10⁹⁡(96-digit number)
72158511003006009462…91447419515095833599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.215 Γ— 10⁹⁡(96-digit number)
72158511003006009462…91447419515095833601
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
1.443 Γ— 10⁹⁢(97-digit number)
14431702200601201892…82894839030191667199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.443 Γ— 10⁹⁢(97-digit number)
14431702200601201892…82894839030191667201
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
2.886 Γ— 10⁹⁢(97-digit number)
28863404401202403785…65789678060383334399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.886 Γ— 10⁹⁢(97-digit number)
28863404401202403785…65789678060383334401
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
5.772 Γ— 10⁹⁢(97-digit number)
57726808802404807570…31579356120766668799
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:57,935,084 XPMΒ·at block #6,836,352 Β· updates every 60s
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