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Block #1,759,761

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2016, 1:50:10 PM Β· Difficulty 10.7319 Β· 5,065,269 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1eeb69209ef0d5b2dab30130977c53429934b33a4a17f6ccee3d87104dffb6e0
View on Chainz β†—

Height

#1,759,761

Difficulty

10.731864

Transactions

2

Size

5.04 KB

Version

2

Bits

0abb5b77

Nonce

148,947,462

Timestamp

9/12/2016, 1:50:10 PM

Confirmations

5,065,269

Mined by

⛏️ P2SHAPq4RSzFwywUognso6xYFWLbSPs1kLwnEi

Merkle Root

48cc05e92b2a4fcdf5339314239ff531e6f8f99e123caf0ae5938cffe8102856
Transactions (2)
Coinbase66c4b096c6e3fb…a6332a62e9d7f5
1 in β†’ 1 out8.7200 XPM110 B
APq4RSzF…s1kLwnEi
d7d73acd5b1fe0…f7b241cc4584d6
33 in β†’ 2 out1.1151 XPM4.85 KB
AUfuWzHo…3PCRLiMvAMvte4Z2…utj4p7u6
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.

2.586 Γ— 10⁹⁷(98-digit number)
25861220060850241981…06303668101422776319
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
2.586 Γ— 10⁹⁷(98-digit number)
25861220060850241981…06303668101422776319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.586 Γ— 10⁹⁷(98-digit number)
25861220060850241981…06303668101422776321
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
5.172 Γ— 10⁹⁷(98-digit number)
51722440121700483962…12607336202845552639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.172 Γ— 10⁹⁷(98-digit number)
51722440121700483962…12607336202845552641
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
1.034 Γ— 10⁹⁸(99-digit number)
10344488024340096792…25214672405691105279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.034 Γ— 10⁹⁸(99-digit number)
10344488024340096792…25214672405691105281
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
2.068 Γ— 10⁹⁸(99-digit number)
20688976048680193584…50429344811382210559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.068 Γ— 10⁹⁸(99-digit number)
20688976048680193584…50429344811382210561
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
4.137 Γ— 10⁹⁸(99-digit number)
41377952097360387169…00858689622764421119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.137 Γ— 10⁹⁸(99-digit number)
41377952097360387169…00858689622764421121
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
8.275 Γ— 10⁹⁸(99-digit number)
82755904194720774339…01717379245528842239
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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