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Block #2,833,159

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 1:39:07 PM Β· Difficulty 11.7148 Β· 4,006,087 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1aca8743cd1559bb5941289d189091910a3182766b9199730d7fb451cde2e8c3
View on Chainz β†—

Height

#2,833,159

Difficulty

11.714754

Transactions

1

Size

200 B

Version

2

Bits

0bb6fa25

Nonce

52,685,631

Timestamp

9/10/2018, 1:39:07 PM

Confirmations

4,006,087

Mined by

⛏️ P2SHAehzad4S7Ud69YARzRXttCegvbbK7zudAR

Merkle Root

a794f4a21672d056b480f32c27b6c49a51453c70a0c6181c0e52a9ddc4f5d12a
Transactions (1)
Coinbasea794f4a21672d0…52a9ddc4f5d12a
1 in β†’ 1 out7.2700 XPM110 B
Aehzad4S…bK7zudAR
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.

7.622 Γ— 10⁹⁴(95-digit number)
76227422025222223039…48531700708835718719
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
7.622 Γ— 10⁹⁴(95-digit number)
76227422025222223039…48531700708835718719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.622 Γ— 10⁹⁴(95-digit number)
76227422025222223039…48531700708835718721
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
1.524 Γ— 10⁹⁡(96-digit number)
15245484405044444607…97063401417671437439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.524 Γ— 10⁹⁡(96-digit number)
15245484405044444607…97063401417671437441
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
3.049 Γ— 10⁹⁡(96-digit number)
30490968810088889215…94126802835342874879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.049 Γ— 10⁹⁡(96-digit number)
30490968810088889215…94126802835342874881
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
6.098 Γ— 10⁹⁡(96-digit number)
60981937620177778431…88253605670685749759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.098 Γ— 10⁹⁡(96-digit number)
60981937620177778431…88253605670685749761
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
1.219 Γ— 10⁹⁢(97-digit number)
12196387524035555686…76507211341371499519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.219 Γ— 10⁹⁢(97-digit number)
12196387524035555686…76507211341371499521
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
2.439 Γ— 10⁹⁢(97-digit number)
24392775048071111372…53014422682742999039
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:57,958,251 XPMΒ·at block #6,839,245 Β· updates every 60s
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