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Block #2,833,286

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 3:39:15 PM Β· Difficulty 11.7152 Β· 4,000,111 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fe8893028338cf5f6b961fc954a81adacaaaf2e19929121ff5496765c3421a05
View on Chainz β†—

Height

#2,833,286

Difficulty

11.715150

Transactions

1

Size

200 B

Version

2

Bits

0bb7141a

Nonce

641,384,544

Timestamp

9/10/2018, 3:39:15 PM

Confirmations

4,000,111

Mined by

⛏️ P2SHANhdfPGbch7AVAHZ6nsXcKaQAiMqAm4YBa

Merkle Root

012dc2f1952da0e9cbb7789f0a63d5f44b9bf8f606e2c33e0fc223b604f0b082
Transactions (1)
Coinbase012dc2f1952da0…c223b604f0b082
1 in β†’ 1 out7.2700 XPM110 B
ANhdfPGb…MqAm4YBa
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.

1.950 Γ— 10⁹⁴(95-digit number)
19506482378744018995…24354319464757985279
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
1.950 Γ— 10⁹⁴(95-digit number)
19506482378744018995…24354319464757985279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.950 Γ— 10⁹⁴(95-digit number)
19506482378744018995…24354319464757985281
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
3.901 Γ— 10⁹⁴(95-digit number)
39012964757488037991…48708638929515970559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.901 Γ— 10⁹⁴(95-digit number)
39012964757488037991…48708638929515970561
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
7.802 Γ— 10⁹⁴(95-digit number)
78025929514976075983…97417277859031941119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.802 Γ— 10⁹⁴(95-digit number)
78025929514976075983…97417277859031941121
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
1.560 Γ— 10⁹⁡(96-digit number)
15605185902995215196…94834555718063882239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.560 Γ— 10⁹⁡(96-digit number)
15605185902995215196…94834555718063882241
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
3.121 Γ— 10⁹⁡(96-digit number)
31210371805990430393…89669111436127764479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.121 Γ— 10⁹⁡(96-digit number)
31210371805990430393…89669111436127764481
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
6.242 Γ— 10⁹⁡(96-digit number)
62420743611980860786…79338222872255528959
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:57,911,376 XPMΒ·at block #6,833,396 Β· updates every 60s
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