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Block #2,767,998

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2018, 8:03:44 PM Β· Difficulty 11.6670 Β· 4,074,935 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
674902eefdc3c55b5777949736fc1fc257a026cfe07e9ab95db0715f24d4d837
View on Chainz β†—

Height

#2,767,998

Difficulty

11.667020

Transactions

2

Size

425 B

Version

2

Bits

0baac1da

Nonce

710,587,268

Timestamp

7/27/2018, 8:03:44 PM

Confirmations

4,074,935

Mined by

⛏️ P2SHAFmuk5pWPG6Y4qw585fGvANemb3LaEVSf3

Merkle Root

1a88122fd5ac206143d7736dc8d11360e7530ea0d07f3126e1f0c36c9d11843b
Transactions (2)
Coinbasec88e3257112ae0…7b7745e13a908b
1 in β†’ 1 out7.3400 XPM110 B
AFmuk5pW…3LaEVSf3
b0bd59890bb98a…83dce8deb60a77
1 in β†’ 2 out7.5656 XPM225 B
AbrZq5aE…Ph1ZfUTGAZZUHjyC…qa3mjrxz
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.

2.875 Γ— 10⁹⁡(96-digit number)
28756259483972869916…83108730769100807999
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
2.875 Γ— 10⁹⁡(96-digit number)
28756259483972869916…83108730769100807999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.875 Γ— 10⁹⁡(96-digit number)
28756259483972869916…83108730769100808001
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
5.751 Γ— 10⁹⁡(96-digit number)
57512518967945739833…66217461538201615999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.751 Γ— 10⁹⁡(96-digit number)
57512518967945739833…66217461538201616001
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
1.150 Γ— 10⁹⁢(97-digit number)
11502503793589147966…32434923076403231999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.150 Γ— 10⁹⁢(97-digit number)
11502503793589147966…32434923076403232001
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
2.300 Γ— 10⁹⁢(97-digit number)
23005007587178295933…64869846152806463999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.300 Γ— 10⁹⁢(97-digit number)
23005007587178295933…64869846152806464001
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
4.601 Γ— 10⁹⁢(97-digit number)
46010015174356591867…29739692305612927999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.601 Γ— 10⁹⁢(97-digit number)
46010015174356591867…29739692305612928001
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
9.202 Γ— 10⁹⁢(97-digit number)
92020030348713183734…59479384611225855999
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:57,987,813 XPMΒ·at block #6,842,932 Β· updates every 60s
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