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Block #2,702,274

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/12/2018, 1:15:43 PM Β· Difficulty 11.6287 Β· 4,131,460 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6cc6d484a8a63001097403e1e504a14a14ba69d91c66e304e8999f5e6078760b
View on Chainz β†—

Height

#2,702,274

Difficulty

11.628739

Transactions

2

Size

725 B

Version

2

Bits

0ba0f510

Nonce

1,315,817,881

Timestamp

6/12/2018, 1:15:43 PM

Confirmations

4,131,460

Mined by

⛏️ P2SHAYgbdcU1jxdK2wQwcLT2unhyLDAdZ9WXZT

Merkle Root

fdd33a3b06d35f8ac60237f1acf86b333fff3916ac6b9e498b53884d3e499c5b
Transactions (2)
Coinbase2eab1ceee1cee5…c29135e0c93387
1 in β†’ 1 out7.3900 XPM109 B
AYgbdcU1…AdZ9WXZT
1aa19e1ea1d538…f37d3f21ccefa7
3 in β†’ 2 out296.0868 XPM524 B
AQmjqzoU…5U6sbve9AbmKF1M2…HJqRp9yW
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.

7.516 Γ— 10⁹⁸(99-digit number)
75164245053620491335…60712457250839183359
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
7.516 Γ— 10⁹⁸(99-digit number)
75164245053620491335…60712457250839183359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.516 Γ— 10⁹⁸(99-digit number)
75164245053620491335…60712457250839183361
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
1.503 Γ— 10⁹⁹(100-digit number)
15032849010724098267…21424914501678366719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.503 Γ— 10⁹⁹(100-digit number)
15032849010724098267…21424914501678366721
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
3.006 Γ— 10⁹⁹(100-digit number)
30065698021448196534…42849829003356733439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.006 Γ— 10⁹⁹(100-digit number)
30065698021448196534…42849829003356733441
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
6.013 Γ— 10⁹⁹(100-digit number)
60131396042896393068…85699658006713466879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.013 Γ— 10⁹⁹(100-digit number)
60131396042896393068…85699658006713466881
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
1.202 Γ— 10¹⁰⁰(101-digit number)
12026279208579278613…71399316013426933759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.202 Γ— 10¹⁰⁰(101-digit number)
12026279208579278613…71399316013426933761
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
2.405 Γ— 10¹⁰⁰(101-digit number)
24052558417158557227…42798632026853867519
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:57,914,096 XPMΒ·at block #6,833,733 Β· updates every 60s
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