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Block #2,832,966

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 10:20:32 AM Β· Difficulty 11.7152 Β· 4,007,369 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3b48d090b8001b457610aea7ba61412f0228ad502c6b5bec794ae16f567b9ba2
View on Chainz β†—

Height

#2,832,966

Difficulty

11.715245

Transactions

1

Size

201 B

Version

2

Bits

0bb71a4b

Nonce

1,038,498,199

Timestamp

9/10/2018, 10:20:32 AM

Confirmations

4,007,369

Mined by

⛏️ P2SHAVdUAf5Ur8Cr3CrJv8F4cF6GeSMLYcqyK6

Merkle Root

d870986478f0e423fc8917c56a4bbbb06d274c891dcd751de41771fa9e4b7323
Transactions (1)
Coinbased870986478f0e4…1771fa9e4b7323
1 in β†’ 1 out7.2700 XPM110 B
AVdUAf5U…MLYcqyK6
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.

5.544 Γ— 10⁹⁢(97-digit number)
55449472576381048019…42657667514876559359
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
5.544 Γ— 10⁹⁢(97-digit number)
55449472576381048019…42657667514876559359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.544 Γ— 10⁹⁢(97-digit number)
55449472576381048019…42657667514876559361
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
1.108 Γ— 10⁹⁷(98-digit number)
11089894515276209603…85315335029753118719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.108 Γ— 10⁹⁷(98-digit number)
11089894515276209603…85315335029753118721
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
2.217 Γ— 10⁹⁷(98-digit number)
22179789030552419207…70630670059506237439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.217 Γ— 10⁹⁷(98-digit number)
22179789030552419207…70630670059506237441
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
4.435 Γ— 10⁹⁷(98-digit number)
44359578061104838415…41261340119012474879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.435 Γ— 10⁹⁷(98-digit number)
44359578061104838415…41261340119012474881
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
8.871 Γ— 10⁹⁷(98-digit number)
88719156122209676830…82522680238024949759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.871 Γ— 10⁹⁷(98-digit number)
88719156122209676830…82522680238024949761
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
1.774 Γ— 10⁹⁸(99-digit number)
17743831224441935366…65045360476049899519
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
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