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Block #2,485,834

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/23/2018, 5:00:05 AM Β· Difficulty 10.9678 Β· 4,356,469 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
092b1d5fb3b7f8cc8a31d663cde1438e80f8731695336f8b51eaef4d8b5b3754
View on Chainz β†—

Height

#2,485,834

Difficulty

10.967816

Transactions

1

Size

200 B

Version

2

Bits

0af7c2c9

Nonce

1,150,199,714

Timestamp

1/23/2018, 5:00:05 AM

Confirmations

4,356,469

Mined by

⛏️ P2SHARsvSFdSt12tz6ob7xiGvctX47b2Z5voVX

Merkle Root

9b404c8156af3d466d2f1d9853336c8b51da53ad84ed44409b907dc86592d58e
Transactions (1)
Coinbase9b404c8156af3d…907dc86592d58e
1 in β†’ 1 out8.3000 XPM110 B
ARsvSFdS…b2Z5voVX
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.

7.356 Γ— 10⁹⁴(95-digit number)
73563659714351988263…82748804854616465279
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
7.356 Γ— 10⁹⁴(95-digit number)
73563659714351988263…82748804854616465279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.356 Γ— 10⁹⁴(95-digit number)
73563659714351988263…82748804854616465281
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
1.471 Γ— 10⁹⁡(96-digit number)
14712731942870397652…65497609709232930559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.471 Γ— 10⁹⁡(96-digit number)
14712731942870397652…65497609709232930561
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
2.942 Γ— 10⁹⁡(96-digit number)
29425463885740795305…30995219418465861119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.942 Γ— 10⁹⁡(96-digit number)
29425463885740795305…30995219418465861121
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
5.885 Γ— 10⁹⁡(96-digit number)
58850927771481590610…61990438836931722239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.885 Γ— 10⁹⁡(96-digit number)
58850927771481590610…61990438836931722241
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
1.177 Γ— 10⁹⁢(97-digit number)
11770185554296318122…23980877673863444479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.177 Γ— 10⁹⁢(97-digit number)
11770185554296318122…23980877673863444481
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
2.354 Γ— 10⁹⁢(97-digit number)
23540371108592636244…47961755347726888959
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:57,982,829 XPMΒ·at block #6,842,302 Β· updates every 60s
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