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Block #2,780,333

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/5/2018, 1:50:38 PM Β· Difficulty 11.6505 Β· 4,052,146 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ba74117bf27ead994eb2a3cbe5076fb6f5636b44c1d3fc7a4eec88bebe1cbfb8
View on Chainz β†—

Height

#2,780,333

Difficulty

11.650511

Transactions

2

Size

3.30 KB

Version

2

Bits

0ba687e9

Nonce

1,059,655,210

Timestamp

8/5/2018, 1:50:38 PM

Confirmations

4,052,146

Mined by

⛏️ P2SHAXEJg1LUtaKsFx1AbJ3r2UzLPiKiUxr9sa

Merkle Root

49d6828afb3ff5813b9c306cfb829d2079ec67af0f04d86fea08470d1248f3e9
Transactions (2)
Coinbase923949958692ff…66417b86583126
1 in β†’ 1 out7.3900 XPM110 B
AXEJg1LU…KiUxr9sa
016703c3af9786…375edc33172ae3
21 in β†’ 2 out1000.0100 XPM3.11 KB
AejmSw8c…t8FLBKoDAJw5ZAK9…znJvTipv
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.

3.178 Γ— 10⁹⁡(96-digit number)
31780899567857811593…94641456746764793599
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
3.178 Γ— 10⁹⁡(96-digit number)
31780899567857811593…94641456746764793599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.178 Γ— 10⁹⁡(96-digit number)
31780899567857811593…94641456746764793601
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
6.356 Γ— 10⁹⁡(96-digit number)
63561799135715623186…89282913493529587199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.356 Γ— 10⁹⁡(96-digit number)
63561799135715623186…89282913493529587201
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
1.271 Γ— 10⁹⁢(97-digit number)
12712359827143124637…78565826987059174399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.271 Γ— 10⁹⁢(97-digit number)
12712359827143124637…78565826987059174401
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
2.542 Γ— 10⁹⁢(97-digit number)
25424719654286249274…57131653974118348799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.542 Γ— 10⁹⁢(97-digit number)
25424719654286249274…57131653974118348801
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
5.084 Γ— 10⁹⁢(97-digit number)
50849439308572498549…14263307948236697599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.084 Γ— 10⁹⁢(97-digit number)
50849439308572498549…14263307948236697601
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
1.016 Γ— 10⁹⁷(98-digit number)
10169887861714499709…28526615896473395199
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:57,903,985 XPMΒ·at block #6,832,478 Β· updates every 60s
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