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Block #2,008,091

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/4/2017, 1:08:55 PM Β· Difficulty 10.7008 Β· 4,832,071 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
38529fb9d099682ce5a4f0eb8ab50332eeea631f089a3708cd758b8129d38b6b
View on Chainz β†—

Height

#2,008,091

Difficulty

10.700773

Transactions

1

Size

200 B

Version

2

Bits

0ab365dd

Nonce

1,294,920,069

Timestamp

3/4/2017, 1:08:55 PM

Confirmations

4,832,071

Mined by

⛏️ P2SHANyh6BB78GexRWyJM7CHUN2FHcN3Qvuoi6

Merkle Root

8b86d6814e033cf39928ed8a083a754afd6e5b383bee3b681ecaa6a71a2ad0e3
Transactions (1)
Coinbase8b86d6814e033c…caa6a71a2ad0e3
1 in β†’ 1 out8.7200 XPM109 B
ANyh6BB7…N3Qvuoi6
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.

1.916 Γ— 10⁹⁸(99-digit number)
19162482965459574708…25116323541043773439
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
1.916 Γ— 10⁹⁸(99-digit number)
19162482965459574708…25116323541043773439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.916 Γ— 10⁹⁸(99-digit number)
19162482965459574708…25116323541043773441
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
3.832 Γ— 10⁹⁸(99-digit number)
38324965930919149417…50232647082087546879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.832 Γ— 10⁹⁸(99-digit number)
38324965930919149417…50232647082087546881
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
7.664 Γ— 10⁹⁸(99-digit number)
76649931861838298835…00465294164175093759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.664 Γ— 10⁹⁸(99-digit number)
76649931861838298835…00465294164175093761
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
1.532 Γ— 10⁹⁹(100-digit number)
15329986372367659767…00930588328350187519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.532 Γ— 10⁹⁹(100-digit number)
15329986372367659767…00930588328350187521
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
3.065 Γ— 10⁹⁹(100-digit number)
30659972744735319534…01861176656700375039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.065 Γ— 10⁹⁹(100-digit number)
30659972744735319534…01861176656700375041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,965,616 XPMΒ·at block #6,840,161 Β· updates every 60s
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