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Block #2,774,425

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/1/2018, 7:33:49 AM Β· Difficulty 11.6657 Β· 4,067,790 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8dc89ee4713bce5540f360cc59a2ab508a896de666698e622314b15a80cc9b31
View on Chainz β†—

Height

#2,774,425

Difficulty

11.665717

Transactions

1

Size

201 B

Version

2

Bits

0baa6c6c

Nonce

1,884,494,390

Timestamp

8/1/2018, 7:33:49 AM

Confirmations

4,067,790

Mined by

⛏️ P2SHAZEhnFEwSxVeRhtCbc64yDvvNagQiasd8U

Merkle Root

52610cd3f5566970f51dec5dd89c94866e7b4b4b1504fe5a207e9b86290b634d
Transactions (1)
Coinbase52610cd3f55669…7e9b86290b634d
1 in β†’ 1 out7.3400 XPM110 B
AZEhnFEw…gQiasd8U
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.

5.479 Γ— 10⁹⁷(98-digit number)
54792625181834231103…29074054740122009599
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
5.479 Γ— 10⁹⁷(98-digit number)
54792625181834231103…29074054740122009599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.479 Γ— 10⁹⁷(98-digit number)
54792625181834231103…29074054740122009601
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
1.095 Γ— 10⁹⁸(99-digit number)
10958525036366846220…58148109480244019199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.095 Γ— 10⁹⁸(99-digit number)
10958525036366846220…58148109480244019201
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
2.191 Γ— 10⁹⁸(99-digit number)
21917050072733692441…16296218960488038399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.191 Γ— 10⁹⁸(99-digit number)
21917050072733692441…16296218960488038401
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
4.383 Γ— 10⁹⁸(99-digit number)
43834100145467384883…32592437920976076799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.383 Γ— 10⁹⁸(99-digit number)
43834100145467384883…32592437920976076801
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
8.766 Γ— 10⁹⁸(99-digit number)
87668200290934769766…65184875841952153599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.766 Γ— 10⁹⁸(99-digit number)
87668200290934769766…65184875841952153601
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
1.753 Γ— 10⁹⁹(100-digit number)
17533640058186953953…30369751683904307199
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:57,982,117 XPMΒ·at block #6,842,214 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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