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Block #2,462,081

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/7/2018, 4:49:17 PM Β· Difficulty 10.9565 Β· 4,342,000 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0709bd8e8abd46d68e3714b50ba1e2fea0e1cf600b1f3cfc7a72d39ba63a815a
View on Chainz β†—

Height

#2,462,081

Difficulty

10.956480

Transactions

2

Size

1.40 KB

Version

2

Bits

0af4dbe4

Nonce

1,033,805,092

Timestamp

1/7/2018, 4:49:17 PM

Confirmations

4,342,000

Mined by

⛏️ P2SHAKvTpjZVUfNVe32j4C8wwdUj4z3HTiMCu4

Merkle Root

3121888aedb0aeb9e6d4e2dad75aee4e81de3074417e7f89dc6c88192dfb00fd
Transactions (2)
Coinbase5cba3d3af54b47…dbac7102dfb890
1 in β†’ 1 out8.3400 XPM110 B
AKvTpjZV…3HTiMCu4
98f96ddb5a3ffc…0af88bfd9807fc
8 in β†’ 1 out40.6706 XPM1.20 KB
AZjuJGi3…MFbdYgjD
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.

1.838 Γ— 10⁹⁴(95-digit number)
18385875156546801361…95138326192374766219
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
1.838 Γ— 10⁹⁴(95-digit number)
18385875156546801361…95138326192374766219
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.838 Γ— 10⁹⁴(95-digit number)
18385875156546801361…95138326192374766221
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
3.677 Γ— 10⁹⁴(95-digit number)
36771750313093602722…90276652384749532439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.677 Γ— 10⁹⁴(95-digit number)
36771750313093602722…90276652384749532441
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
7.354 Γ— 10⁹⁴(95-digit number)
73543500626187205445…80553304769499064879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.354 Γ— 10⁹⁴(95-digit number)
73543500626187205445…80553304769499064881
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
1.470 Γ— 10⁹⁡(96-digit number)
14708700125237441089…61106609538998129759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.470 Γ— 10⁹⁡(96-digit number)
14708700125237441089…61106609538998129761
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
2.941 Γ— 10⁹⁡(96-digit number)
29417400250474882178…22213219077996259519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.941 Γ— 10⁹⁡(96-digit number)
29417400250474882178…22213219077996259521
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
5.883 Γ— 10⁹⁡(96-digit number)
58834800500949764356…44426438155992519039
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:57,676,697 XPMΒ·at block #6,804,080 Β· updates every 60s
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