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Block #2,785,622

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2018, 12:41:39 AM Β· Difficulty 11.6719 Β· 4,053,221 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
16bc64128ddbb8f8a64e0a9b200b9583ed4e0934d830588fe802cdde8092c390
View on Chainz β†—

Height

#2,785,622

Difficulty

11.671934

Transactions

1

Size

200 B

Version

2

Bits

0bac03d9

Nonce

899,067,421

Timestamp

8/9/2018, 12:41:39 AM

Confirmations

4,053,221

Mined by

⛏️ P2SHAV8pW6xsDh5rKE9KKGQdTAEoDFCmuVVGGq

Merkle Root

1acd589e806813c118d9053895628441d0ac8ae36a21f9ff0a86df10871eb703
Transactions (1)
Coinbase1acd589e806813…86df10871eb703
1 in β†’ 1 out7.3300 XPM110 B
AV8pW6xs…CmuVVGGq
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.

5.582 Γ— 10⁹³(94-digit number)
55823759938607052384…29622909772843886079
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
5.582 Γ— 10⁹³(94-digit number)
55823759938607052384…29622909772843886079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.582 Γ— 10⁹³(94-digit number)
55823759938607052384…29622909772843886081
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
1.116 Γ— 10⁹⁴(95-digit number)
11164751987721410476…59245819545687772159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.116 Γ— 10⁹⁴(95-digit number)
11164751987721410476…59245819545687772161
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
2.232 Γ— 10⁹⁴(95-digit number)
22329503975442820953…18491639091375544319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.232 Γ— 10⁹⁴(95-digit number)
22329503975442820953…18491639091375544321
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
4.465 Γ— 10⁹⁴(95-digit number)
44659007950885641907…36983278182751088639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.465 Γ— 10⁹⁴(95-digit number)
44659007950885641907…36983278182751088641
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
8.931 Γ— 10⁹⁴(95-digit number)
89318015901771283815…73966556365502177279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.931 Γ— 10⁹⁴(95-digit number)
89318015901771283815…73966556365502177281
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
1.786 Γ— 10⁹⁡(96-digit number)
17863603180354256763…47933112731004354559
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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