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Block #2,821,054

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2018, 7:51:46 AM Β· Difficulty 11.7006 Β· 4,021,245 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cf387a86fe09e7a62777761122cd6cea4d806704fc7973a236538c673ffc95b9
View on Chainz β†—

Height

#2,821,054

Difficulty

11.700599

Transactions

2

Size

1.28 KB

Version

2

Bits

0bb35a73

Nonce

523,019,989

Timestamp

9/2/2018, 7:51:46 AM

Confirmations

4,021,245

Mined by

⛏️ P2SHAXtQf5o5oQUQNURDQdCkJcoVUCf9GMhZ2t

Merkle Root

376b565a04e76de3d89f8c394b83a0875ed57c7fa3313dcb3b9c55a4a40afb81
Transactions (2)
Coinbased0720ecab013f0…7875eec39a8bdd
1 in β†’ 1 out7.3100 XPM110 B
AXtQf5o5…f9GMhZ2t
d50c404de7d062…30e0673204fbe9
7 in β†’ 2 out60.0300 XPM1.09 KB
ALh5G3Np…6TsNC2wjAYHYFGkE…8inpw9WJ
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.

3.609 Γ— 10⁹¹(92-digit number)
36097584190812238512…74345736135087883039
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
3.609 Γ— 10⁹¹(92-digit number)
36097584190812238512…74345736135087883039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.609 Γ— 10⁹¹(92-digit number)
36097584190812238512…74345736135087883041
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
7.219 Γ— 10⁹¹(92-digit number)
72195168381624477024…48691472270175766079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.219 Γ— 10⁹¹(92-digit number)
72195168381624477024…48691472270175766081
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
1.443 Γ— 10⁹²(93-digit number)
14439033676324895404…97382944540351532159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.443 Γ— 10⁹²(93-digit number)
14439033676324895404…97382944540351532161
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
2.887 Γ— 10⁹²(93-digit number)
28878067352649790809…94765889080703064319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.887 Γ— 10⁹²(93-digit number)
28878067352649790809…94765889080703064321
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
5.775 Γ— 10⁹²(93-digit number)
57756134705299581619…89531778161406128639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.775 Γ— 10⁹²(93-digit number)
57756134705299581619…89531778161406128641
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
1.155 Γ— 10⁹³(94-digit number)
11551226941059916323…79063556322812257279
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:57,982,796 XPMΒ·at block #6,842,298 Β· updates every 60s
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