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Block #2,833,073

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 12:14:18 PM Β· Difficulty 11.7147 Β· 4,009,908 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
70aa6d10623ea6d5c89229e0477f83d822b35aae190717b980981a1e02bf87bc
View on Chainz β†—

Height

#2,833,073

Difficulty

11.714706

Transactions

1

Size

200 B

Version

2

Bits

0bb6f6fa

Nonce

519,664,680

Timestamp

9/10/2018, 12:14:18 PM

Confirmations

4,009,908

Mined by

⛏️ P2SHAeA2RoGsKPgmc45x1KgD18Yhm5PDT6Kq9G

Merkle Root

8b2cde7aac32854c6dc1918560e279a4b49917869e3634798d30b9d3539ce9ea
Transactions (1)
Coinbase8b2cde7aac3285…30b9d3539ce9ea
1 in β†’ 1 out7.2700 XPM110 B
AeA2RoGs…PDT6Kq9G
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.

2.913 Γ— 10⁹³(94-digit number)
29138777296518742290…69570847335489336489
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
2.913 Γ— 10⁹³(94-digit number)
29138777296518742290…69570847335489336489
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.913 Γ— 10⁹³(94-digit number)
29138777296518742290…69570847335489336491
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
5.827 Γ— 10⁹³(94-digit number)
58277554593037484580…39141694670978672979
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.827 Γ— 10⁹³(94-digit number)
58277554593037484580…39141694670978672981
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
1.165 Γ— 10⁹⁴(95-digit number)
11655510918607496916…78283389341957345959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.165 Γ— 10⁹⁴(95-digit number)
11655510918607496916…78283389341957345961
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
2.331 Γ— 10⁹⁴(95-digit number)
23311021837214993832…56566778683914691919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.331 Γ— 10⁹⁴(95-digit number)
23311021837214993832…56566778683914691921
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
4.662 Γ— 10⁹⁴(95-digit number)
46622043674429987664…13133557367829383839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.662 Γ— 10⁹⁴(95-digit number)
46622043674429987664…13133557367829383841
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
9.324 Γ— 10⁹⁴(95-digit number)
93244087348859975328…26267114735658767679
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:57,988,202 XPMΒ·at block #6,842,980 Β· updates every 60s
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