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Block #2,853,022

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/24/2018, 8:00:24 AM Β· Difficulty 11.7179 Β· 3,986,647 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c3189def12bcdb04a0dc35e3ca2a69efdb51727f6e680ef36524194ecb2de085
View on Chainz β†—

Height

#2,853,022

Difficulty

11.717871

Transactions

1

Size

201 B

Version

2

Bits

0bb7c66a

Nonce

299,400,082

Timestamp

9/24/2018, 8:00:24 AM

Confirmations

3,986,647

Mined by

⛏️ P2SHASbUwsc1uUecmQ69vfHcXTaK2WngUKKQ8g

Merkle Root

386a6cce53e6e5ff2c52df760208a062cc1481778fa68009d643c2188cfa8cc3
Transactions (1)
Coinbase386a6cce53e6e5…43c2188cfa8cc3
1 in β†’ 1 out7.2700 XPM110 B
ASbUwsc1…ngUKKQ8g
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.

1.330 Γ— 10⁹⁢(97-digit number)
13303914912281005058…66342718211160596479
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
1.330 Γ— 10⁹⁢(97-digit number)
13303914912281005058…66342718211160596479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.330 Γ— 10⁹⁢(97-digit number)
13303914912281005058…66342718211160596481
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
2.660 Γ— 10⁹⁢(97-digit number)
26607829824562010117…32685436422321192959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.660 Γ— 10⁹⁢(97-digit number)
26607829824562010117…32685436422321192961
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
5.321 Γ— 10⁹⁢(97-digit number)
53215659649124020235…65370872844642385919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.321 Γ— 10⁹⁢(97-digit number)
53215659649124020235…65370872844642385921
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
1.064 Γ— 10⁹⁷(98-digit number)
10643131929824804047…30741745689284771839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.064 Γ— 10⁹⁷(98-digit number)
10643131929824804047…30741745689284771841
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
2.128 Γ— 10⁹⁷(98-digit number)
21286263859649608094…61483491378569543679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.128 Γ— 10⁹⁷(98-digit number)
21286263859649608094…61483491378569543681
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
4.257 Γ— 10⁹⁷(98-digit number)
42572527719299216188…22966982757139087359
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:57,961,649 XPMΒ·at block #6,839,668 Β· updates every 60s
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