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Block #2,783,153

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2018, 10:09:51 AM Β· Difficulty 11.6614

TWN
Bi-Twin Chain

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

Block Header
Block Hash
69719219d2de73d9dfb5c2e43d90fd5e6a961fa7b5d40d5c51a3e653ad9eb63f
View on Chainz β†—

Height

#2,783,153

Difficulty

11.661403

Transactions

Timestamp

8/7/2018, 10:09:51 AM

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.

5.340 Γ— 10⁹⁴(95-digit number)
53400811491060332182…89317364888679763839
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
5.340 Γ— 10⁹⁴(95-digit number)
53400811491060332182…89317364888679763839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.340 Γ— 10⁹⁴(95-digit number)
53400811491060332182…89317364888679763841
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
1.068 Γ— 10⁹⁡(96-digit number)
10680162298212066436…78634729777359527679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.068 Γ— 10⁹⁡(96-digit number)
10680162298212066436…78634729777359527681
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
2.136 Γ— 10⁹⁡(96-digit number)
21360324596424132872…57269459554719055359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.136 Γ— 10⁹⁡(96-digit number)
21360324596424132872…57269459554719055361
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
4.272 Γ— 10⁹⁡(96-digit number)
42720649192848265745…14538919109438110719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.272 Γ— 10⁹⁡(96-digit number)
42720649192848265745…14538919109438110721
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
8.544 Γ— 10⁹⁡(96-digit number)
85441298385696531491…29077838218876221439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.544 Γ— 10⁹⁡(96-digit number)
85441298385696531491…29077838218876221441
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
1.708 Γ— 10⁹⁢(97-digit number)
17088259677139306298…58155676437752442879
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
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