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Block #2,818,212

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2018, 9:28:12 AM Β· Difficulty 11.6970 Β· 4,023,864 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2cea91703926824457acf904a59fea01255195209437bb1dec11f3858a6c1b0c
View on Chainz β†—

Height

#2,818,212

Difficulty

11.696985

Transactions

1

Size

199 B

Version

2

Bits

0bb26d98

Nonce

2,003,652,693

Timestamp

8/31/2018, 9:28:12 AM

Confirmations

4,023,864

Mined by

⛏️ P2SHAN3SNQcuYYiAF4Q9XEbrC3eGZA9X2nAdfo

Merkle Root

ec02bee156f59a19bbd40df0f1569cfef87ec460e52ca55294c41f5c176ca63b
Transactions (1)
Coinbaseec02bee156f59a…c41f5c176ca63b
1 in β†’ 1 out7.3000 XPM110 B
AN3SNQcu…9X2nAdfo
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.

1.365 Γ— 10⁹³(94-digit number)
13652075080235598096…98958331737228680839
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
1.365 Γ— 10⁹³(94-digit number)
13652075080235598096…98958331737228680839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.365 Γ— 10⁹³(94-digit number)
13652075080235598096…98958331737228680841
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
2.730 Γ— 10⁹³(94-digit number)
27304150160471196193…97916663474457361679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.730 Γ— 10⁹³(94-digit number)
27304150160471196193…97916663474457361681
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
5.460 Γ— 10⁹³(94-digit number)
54608300320942392386…95833326948914723359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.460 Γ— 10⁹³(94-digit number)
54608300320942392386…95833326948914723361
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
1.092 Γ— 10⁹⁴(95-digit number)
10921660064188478477…91666653897829446719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.092 Γ— 10⁹⁴(95-digit number)
10921660064188478477…91666653897829446721
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
2.184 Γ— 10⁹⁴(95-digit number)
21843320128376956954…83333307795658893439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.184 Γ— 10⁹⁴(95-digit number)
21843320128376956954…83333307795658893441
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
4.368 Γ— 10⁹⁴(95-digit number)
43686640256753913908…66666615591317786879
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:57,980,993 XPMΒ·at block #6,842,075 Β· updates every 60s
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