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Block #2,833,106

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 12:49:47 PM Β· Difficulty 11.7146 Β· 4,005,470 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1082c0019a116eaec5f5cc717f70c6cc689f093325cd0443b89b8804ced1aeb6
View on Chainz β†—

Height

#2,833,106

Difficulty

11.714603

Transactions

1

Size

200 B

Version

2

Bits

0bb6f032

Nonce

790,625,848

Timestamp

9/10/2018, 12:49:47 PM

Confirmations

4,005,470

Mined by

⛏️ P2SHAUwo7h9Upue58f5tvCEDYFmxVfMTTyrFzP

Merkle Root

aa486254db2e2ddd1795d9378a0da0b3c00cd40f3083bd5cdf4c93fc61c813a6
Transactions (1)
Coinbaseaa486254db2e2d…4c93fc61c813a6
1 in β†’ 1 out7.2700 XPM110 B
AUwo7h9U…MTTyrFzP
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.

1.461 Γ— 10⁹⁴(95-digit number)
14618870102028772342…68798097727282265039
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
1.461 Γ— 10⁹⁴(95-digit number)
14618870102028772342…68798097727282265039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.461 Γ— 10⁹⁴(95-digit number)
14618870102028772342…68798097727282265041
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
2.923 Γ— 10⁹⁴(95-digit number)
29237740204057544684…37596195454564530079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.923 Γ— 10⁹⁴(95-digit number)
29237740204057544684…37596195454564530081
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
5.847 Γ— 10⁹⁴(95-digit number)
58475480408115089369…75192390909129060159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.847 Γ— 10⁹⁴(95-digit number)
58475480408115089369…75192390909129060161
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
1.169 Γ— 10⁹⁡(96-digit number)
11695096081623017873…50384781818258120319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.169 Γ— 10⁹⁡(96-digit number)
11695096081623017873…50384781818258120321
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
2.339 Γ— 10⁹⁡(96-digit number)
23390192163246035747…00769563636516240639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.339 Γ— 10⁹⁡(96-digit number)
23390192163246035747…00769563636516240641
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
4.678 Γ— 10⁹⁡(96-digit number)
46780384326492071495…01539127273032481279
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:57,952,894 XPMΒ·at block #6,838,575 Β· updates every 60s
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