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Block #2,288,110

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2017, 5:31:18 PM Β· Difficulty 10.9556 Β· 4,538,867 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d0a2669c71e2e978ee3c1e222e798d58d3c8317523ea36103191c747946343e
View on Chainz β†—

Height

#2,288,110

Difficulty

10.955559

Transactions

2

Size

1020 B

Version

2

Bits

0af49f85

Nonce

1,079,324,944

Timestamp

9/8/2017, 5:31:18 PM

Confirmations

4,538,867

Mined by

⛏️ P2SHALihK9v8KzYenw7Lg3tetmCwTESAiBBcBD

Merkle Root

f67abda0a6d28fdc692d8ca2d4217392ecf18b48fadd3d8b97844c421f6bfd27
Transactions (2)
Coinbaseab001844d441bd…b097482ce49c40
1 in β†’ 1 out8.3300 XPM110 B
ALihK9v8…SAiBBcBD
6fe5063cd1dd78…0dfc6e196495af
5 in β†’ 2 out2000.0100 XPM820 B
AdqqP8ZY…fK1tY9z9ARaNCeSx…b8M3uhxY
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.

4.164 Γ— 10⁹⁴(95-digit number)
41648435765959715125…06686218704311661379
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
4.164 Γ— 10⁹⁴(95-digit number)
41648435765959715125…06686218704311661379
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.164 Γ— 10⁹⁴(95-digit number)
41648435765959715125…06686218704311661381
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
8.329 Γ— 10⁹⁴(95-digit number)
83296871531919430251…13372437408623322759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.329 Γ— 10⁹⁴(95-digit number)
83296871531919430251…13372437408623322761
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
1.665 Γ— 10⁹⁡(96-digit number)
16659374306383886050…26744874817246645519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.665 Γ— 10⁹⁡(96-digit number)
16659374306383886050…26744874817246645521
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
3.331 Γ— 10⁹⁡(96-digit number)
33318748612767772100…53489749634493291039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.331 Γ— 10⁹⁡(96-digit number)
33318748612767772100…53489749634493291041
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
6.663 Γ— 10⁹⁡(96-digit number)
66637497225535544201…06979499268986582079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.663 Γ— 10⁹⁡(96-digit number)
66637497225535544201…06979499268986582081
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
1.332 Γ— 10⁹⁢(97-digit number)
13327499445107108840…13958998537973164159
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:57,859,991 XPMΒ·at block #6,826,976 Β· updates every 60s
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