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Block #2,473,058

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/14/2018, 6:25:48 PM Β· Difficulty 10.9632 Β· 4,368,825 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a423e7074187154d7bdca704510d52a7bfaf4999f21c256f80dc510114796dd1
View on Chainz β†—

Height

#2,473,058

Difficulty

10.963182

Transactions

2

Size

1019 B

Version

2

Bits

0af69311

Nonce

246,525,468

Timestamp

1/14/2018, 6:25:48 PM

Confirmations

4,368,825

Mined by

⛏️ P2SHAYwFYdJPjHjBxcDkuSBifJWPzid9Vrbu4M

Merkle Root

1f93a5fca66799e92c4a4446c72c4ee1de5ce3ec9460781f27c6db2503769772
Transactions (2)
Coinbase6a332a5423cf59…bb2b5b634c7df4
1 in β†’ 1 out8.3200 XPM109 B
AYwFYdJP…d9Vrbu4M
aa10d3fbe49274…f163e3a79626a3
5 in β†’ 2 out240.0307 XPM820 B
AQV2cMEF…SFfb2zE5AMw7msjY…kT3kGoJ9
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.

6.808 Γ— 10⁹³(94-digit number)
68083071943409564561…30806392032995020879
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
6.808 Γ— 10⁹³(94-digit number)
68083071943409564561…30806392032995020879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.808 Γ— 10⁹³(94-digit number)
68083071943409564561…30806392032995020881
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
1.361 Γ— 10⁹⁴(95-digit number)
13616614388681912912…61612784065990041759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.361 Γ— 10⁹⁴(95-digit number)
13616614388681912912…61612784065990041761
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
2.723 Γ— 10⁹⁴(95-digit number)
27233228777363825824…23225568131980083519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.723 Γ— 10⁹⁴(95-digit number)
27233228777363825824…23225568131980083521
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
5.446 Γ— 10⁹⁴(95-digit number)
54466457554727651649…46451136263960167039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.446 Γ— 10⁹⁴(95-digit number)
54466457554727651649…46451136263960167041
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
1.089 Γ— 10⁹⁡(96-digit number)
10893291510945530329…92902272527920334079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.089 Γ— 10⁹⁡(96-digit number)
10893291510945530329…92902272527920334081
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
2.178 Γ— 10⁹⁡(96-digit number)
21786583021891060659…85804545055840668159
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:57,979,440 XPMΒ·at block #6,841,882 Β· updates every 60s
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