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Block #3,002,673

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/9/2019, 10:31:42 PM Β· Difficulty 11.2024 Β· 3,841,829 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4e849f7a5756bf28aa3e73012863071d02d462c1daff19051c9e2443d6690431
View on Chainz β†—

Height

#3,002,673

Difficulty

11.202364

Transactions

1

Size

200 B

Version

2

Bits

0b33ce24

Nonce

680,339,967

Timestamp

1/9/2019, 10:31:42 PM

Confirmations

3,841,829

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

a8d9337dfd707164066a0350829448136908045368a3c766a05d7cd88f4f2b0f
Transactions (1)
Coinbasea8d9337dfd7071…5d7cd88f4f2b0f
1 in β†’ 1 out7.9600 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.

8.657 Γ— 10⁹⁴(95-digit number)
86573415055128629287…24868823917133190399
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
8.657 Γ— 10⁹⁴(95-digit number)
86573415055128629287…24868823917133190399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.657 Γ— 10⁹⁴(95-digit number)
86573415055128629287…24868823917133190401
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
1.731 Γ— 10⁹⁡(96-digit number)
17314683011025725857…49737647834266380799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.731 Γ— 10⁹⁡(96-digit number)
17314683011025725857…49737647834266380801
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
3.462 Γ— 10⁹⁡(96-digit number)
34629366022051451714…99475295668532761599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.462 Γ— 10⁹⁡(96-digit number)
34629366022051451714…99475295668532761601
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
6.925 Γ— 10⁹⁡(96-digit number)
69258732044102903429…98950591337065523199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.925 Γ— 10⁹⁡(96-digit number)
69258732044102903429…98950591337065523201
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
1.385 Γ— 10⁹⁢(97-digit number)
13851746408820580685…97901182674131046399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.385 Γ— 10⁹⁢(97-digit number)
13851746408820580685…97901182674131046401
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
2.770 Γ— 10⁹⁢(97-digit number)
27703492817641161371…95802365348262092799
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:58,000,413 XPMΒ·at block #6,844,501 Β· updates every 60s
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