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Block #2,924,889

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2018, 3:33:43 AM Β· Difficulty 11.3570 Β· 3,920,487 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d338e6b8a15c4ddab4d2a157f76de98e13b6d6e1dd77d325df492280deb89cd0
View on Chainz β†—

Height

#2,924,889

Difficulty

11.357020

Transactions

1

Size

201 B

Version

2

Bits

0b5b65a7

Nonce

779,679,388

Timestamp

11/16/2018, 3:33:43 AM

Confirmations

3,920,487

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

bad0de0710c49f798cd9992131553e8813905da6159a59d4db3b9cd77f7cc5e7
Transactions (1)
Coinbasebad0de0710c49f…3b9cd77f7cc5e7
1 in β†’ 1 out7.7400 XPM110 B
AbXwmGxD…4XXYP765
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.

1.589 Γ— 10⁹⁢(97-digit number)
15894078309434046201…82096620349795205119
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
1.589 Γ— 10⁹⁢(97-digit number)
15894078309434046201…82096620349795205119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.589 Γ— 10⁹⁢(97-digit number)
15894078309434046201…82096620349795205121
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
3.178 Γ— 10⁹⁢(97-digit number)
31788156618868092402…64193240699590410239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.178 Γ— 10⁹⁢(97-digit number)
31788156618868092402…64193240699590410241
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
6.357 Γ— 10⁹⁢(97-digit number)
63576313237736184804…28386481399180820479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.357 Γ— 10⁹⁢(97-digit number)
63576313237736184804…28386481399180820481
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
1.271 Γ— 10⁹⁷(98-digit number)
12715262647547236960…56772962798361640959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.271 Γ— 10⁹⁷(98-digit number)
12715262647547236960…56772962798361640961
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
2.543 Γ— 10⁹⁷(98-digit number)
25430525295094473921…13545925596723281919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.543 Γ— 10⁹⁷(98-digit number)
25430525295094473921…13545925596723281921
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
5.086 Γ— 10⁹⁷(98-digit number)
50861050590188947843…27091851193446563839
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:58,007,452 XPMΒ·at block #6,845,375 Β· updates every 60s
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