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Block #2,719,789

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 6/24/2018, 8:50:27 PM Β· Difficulty 11.6129 Β· 4,122,674 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27582e2770b80a9fe7aa90153c2a58cabdfd0f834dfbd93ca26ebfcb7919fbaf
View on Chainz β†—

Height

#2,719,789

Difficulty

11.612852

Transactions

1

Size

200 B

Version

2

Bits

0b9ce3d6

Nonce

169,835,820

Timestamp

6/24/2018, 8:50:27 PM

Confirmations

4,122,674

Mined by

⛏️ P2SHALuizqG6kRPEf6mp2iSLHVWCLffVE9CLPj

Merkle Root

d5a86681f489901e7d50418dd20b24547ed9c0236fe9df2cd425556bfa70d098
Transactions (1)
Coinbased5a86681f48990…25556bfa70d098
1 in β†’ 1 out7.4000 XPM110 B
ALuizqG6…fVE9CLPj
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.

4.718 Γ— 10⁹³(94-digit number)
47184692490201094496…04661131719625267199
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
4.718 Γ— 10⁹³(94-digit number)
47184692490201094496…04661131719625267199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.718 Γ— 10⁹³(94-digit number)
47184692490201094496…04661131719625267201
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
9.436 Γ— 10⁹³(94-digit number)
94369384980402188992…09322263439250534399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.436 Γ— 10⁹³(94-digit number)
94369384980402188992…09322263439250534401
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
1.887 Γ— 10⁹⁴(95-digit number)
18873876996080437798…18644526878501068799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.887 Γ— 10⁹⁴(95-digit number)
18873876996080437798…18644526878501068801
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
3.774 Γ— 10⁹⁴(95-digit number)
37747753992160875596…37289053757002137599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.774 Γ— 10⁹⁴(95-digit number)
37747753992160875596…37289053757002137601
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
7.549 Γ— 10⁹⁴(95-digit number)
75495507984321751193…74578107514004275199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.549 Γ— 10⁹⁴(95-digit number)
75495507984321751193…74578107514004275201
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
1.509 Γ— 10⁹⁡(96-digit number)
15099101596864350238…49156215028008550399
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.509 Γ— 10⁹⁡(96-digit number)
15099101596864350238…49156215028008550401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,984,122 XPMΒ·at block #6,842,462 Β· updates every 60s
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