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Block #2,754,434

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2018, 12:19:28 PM Β· Difficulty 11.6571 Β· 4,086,924 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c31c1cab78fd5c0956fd99bd5ce584eafbfa057aeb7ba0c3b0224ce95526cd15
View on Chainz β†—

Height

#2,754,434

Difficulty

11.657092

Transactions

1

Size

201 B

Version

2

Bits

0ba83730

Nonce

1,615,164,377

Timestamp

7/18/2018, 12:19:28 PM

Confirmations

4,086,924

Mined by

⛏️ P2SHAevHU4Hpfwn2GRhUKHGbW599Gvq8oFRGQW

Merkle Root

fdf49ded076419bf345601778d8abb9fc017bc13c310d8121eedf56f036a7a64
Transactions (1)
Coinbasefdf49ded076419…edf56f036a7a64
1 in β†’ 1 out7.3500 XPM110 B
AevHU4Hp…q8oFRGQW
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.

1.232 Γ— 10⁹⁷(98-digit number)
12324284668176251439…40261406791754521599
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
1.232 Γ— 10⁹⁷(98-digit number)
12324284668176251439…40261406791754521599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.232 Γ— 10⁹⁷(98-digit number)
12324284668176251439…40261406791754521601
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
2.464 Γ— 10⁹⁷(98-digit number)
24648569336352502878…80522813583509043199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.464 Γ— 10⁹⁷(98-digit number)
24648569336352502878…80522813583509043201
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
4.929 Γ— 10⁹⁷(98-digit number)
49297138672705005756…61045627167018086399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.929 Γ— 10⁹⁷(98-digit number)
49297138672705005756…61045627167018086401
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
9.859 Γ— 10⁹⁷(98-digit number)
98594277345410011512…22091254334036172799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.859 Γ— 10⁹⁷(98-digit number)
98594277345410011512…22091254334036172801
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
1.971 Γ— 10⁹⁸(99-digit number)
19718855469082002302…44182508668072345599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.971 Γ— 10⁹⁸(99-digit number)
19718855469082002302…44182508668072345601
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
3.943 Γ— 10⁹⁸(99-digit number)
39437710938164004605…88365017336144691199
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:57,975,232 XPMΒ·at block #6,841,357 Β· updates every 60s
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