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Block #2,683,933

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/30/2018, 4:01:36 AM Β· Difficulty 11.6910 Β· 4,154,344 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
64100d75a393be566100dddf8554b1c13672adcb1830da643dfbec35d114089a
View on Chainz β†—

Height

#2,683,933

Difficulty

11.691027

Transactions

3

Size

619 B

Version

2

Bits

0bb0e720

Nonce

199,533,587

Timestamp

5/30/2018, 4:01:36 AM

Confirmations

4,154,344

Mined by

⛏️ P2SHAR51KgD5AMJqWGxJAKDxJeSdKE6dfQU9WT

Merkle Root

09e57f0af408af1f26b04b89459793166c8f2efd3fc6d88b664b47f418aa4937
Transactions (3)
Coinbase97dc850926283f…4049a23d74f42f
1 in β†’ 1 out7.3209 XPM110 B
AR51KgD5…6dfQU9WT
0eb61db1e87fd6…7e4ca1a75378d9
1 in β†’ 2 out1.1265 XPM227 B
AHM4Lkw2…NaayHpzTAdRyi4Ls…BbJJ6nGF
a6d0f3e13c86d5…107f0b7950917d
1 in β†’ 1 out5.0000 XPM192 B
AbW8AKqG…47YJwoPc
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.

5.414 Γ— 10⁹⁡(96-digit number)
54141522452260709350…74318791581449839519
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
5.414 Γ— 10⁹⁡(96-digit number)
54141522452260709350…74318791581449839519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.414 Γ— 10⁹⁡(96-digit number)
54141522452260709350…74318791581449839521
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
1.082 Γ— 10⁹⁢(97-digit number)
10828304490452141870…48637583162899679039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.082 Γ— 10⁹⁢(97-digit number)
10828304490452141870…48637583162899679041
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
2.165 Γ— 10⁹⁢(97-digit number)
21656608980904283740…97275166325799358079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.165 Γ— 10⁹⁢(97-digit number)
21656608980904283740…97275166325799358081
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
4.331 Γ— 10⁹⁢(97-digit number)
43313217961808567480…94550332651598716159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.331 Γ— 10⁹⁢(97-digit number)
43313217961808567480…94550332651598716161
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
8.662 Γ— 10⁹⁢(97-digit number)
86626435923617134961…89100665303197432319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.662 Γ— 10⁹⁢(97-digit number)
86626435923617134961…89100665303197432321
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
1.732 Γ— 10⁹⁷(98-digit number)
17325287184723426992…78201330606394864639
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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