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Block #2,548,141

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/4/2018, 5:47:48 AM Β· Difficulty 10.9885 Β· 4,297,062 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
85e16ee7e6d8a67d5352523c92fcca096b9a353b2bc963df843bbcb70d4e3518
View on Chainz β†—

Height

#2,548,141

Difficulty

10.988479

Transactions

2

Size

1.14 KB

Version

2

Bits

0afd0cf4

Nonce

524,869,339

Timestamp

3/4/2018, 5:47:48 AM

Confirmations

4,297,062

Mined by

⛏️ P2SHAY8ZvxkSMwhxzNqz1n3UP3wEFZcdLW3ff2

Merkle Root

0135ec114b2b31e9b1013429581e590d35d55a72d0689622f66ba0f48f0b3e33
Transactions (2)
Coinbaseeff754e1caaa73…1ae4e59dc5b459
1 in β†’ 1 out8.2800 XPM110 B
AY8ZvxkS…cdLW3ff2
d948d92d8937f8…1d120792cb4bd0
6 in β†’ 2 out20.6900 XPM965 B
AXFArXwD…ZjT5Juh6AJxGJ7TH…3ipMXzh3
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.

2.069 Γ— 10⁹⁴(95-digit number)
20693810687010707424…18723647450148307839
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
2.069 Γ— 10⁹⁴(95-digit number)
20693810687010707424…18723647450148307839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.069 Γ— 10⁹⁴(95-digit number)
20693810687010707424…18723647450148307841
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
4.138 Γ— 10⁹⁴(95-digit number)
41387621374021414848…37447294900296615679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.138 Γ— 10⁹⁴(95-digit number)
41387621374021414848…37447294900296615681
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
8.277 Γ— 10⁹⁴(95-digit number)
82775242748042829696…74894589800593231359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.277 Γ— 10⁹⁴(95-digit number)
82775242748042829696…74894589800593231361
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
1.655 Γ— 10⁹⁡(96-digit number)
16555048549608565939…49789179601186462719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.655 Γ— 10⁹⁡(96-digit number)
16555048549608565939…49789179601186462721
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
3.311 Γ— 10⁹⁡(96-digit number)
33110097099217131878…99578359202372925439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.311 Γ— 10⁹⁡(96-digit number)
33110097099217131878…99578359202372925441
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
6.622 Γ— 10⁹⁡(96-digit number)
66220194198434263757…99156718404745850879
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:58,006,057 XPMΒ·at block #6,845,202 Β· updates every 60s
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