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Block #2,833,202

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 2:20:39 PM Β· Difficulty 11.7149 Β· 4,005,611 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9baa8bab98c032e310b939835d90966755018e75fc2f21e428571b9ee33e4186
View on Chainz β†—

Height

#2,833,202

Difficulty

11.714859

Transactions

1

Size

201 B

Version

2

Bits

0bb70106

Nonce

552,238,913

Timestamp

9/10/2018, 2:20:39 PM

Confirmations

4,005,611

Mined by

⛏️ P2SHAZWH22FarMyKqQg9MDHxgkgJnWPX613zRD

Merkle Root

92a81f7924d29eb1839a820597c7803ee7c39f6d501e302a50385b852a913ba8
Transactions (1)
Coinbase92a81f7924d29e…385b852a913ba8
1 in β†’ 1 out7.2700 XPM110 B
AZWH22Fa…PX613zRD
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.

1.973 Γ— 10⁹⁢(97-digit number)
19732897056523385748…61985833670487815199
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
1.973 Γ— 10⁹⁢(97-digit number)
19732897056523385748…61985833670487815199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.973 Γ— 10⁹⁢(97-digit number)
19732897056523385748…61985833670487815201
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
3.946 Γ— 10⁹⁢(97-digit number)
39465794113046771497…23971667340975630399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.946 Γ— 10⁹⁢(97-digit number)
39465794113046771497…23971667340975630401
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
7.893 Γ— 10⁹⁢(97-digit number)
78931588226093542994…47943334681951260799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.893 Γ— 10⁹⁢(97-digit number)
78931588226093542994…47943334681951260801
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
1.578 Γ— 10⁹⁷(98-digit number)
15786317645218708598…95886669363902521599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.578 Γ— 10⁹⁷(98-digit number)
15786317645218708598…95886669363902521601
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
3.157 Γ— 10⁹⁷(98-digit number)
31572635290437417197…91773338727805043199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.157 Γ— 10⁹⁷(98-digit number)
31572635290437417197…91773338727805043201
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
6.314 Γ— 10⁹⁷(98-digit number)
63145270580874834395…83546677455610086399
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:57,954,769 XPMΒ·at block #6,838,812 Β· updates every 60s
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