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Block #1,853,195

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/17/2016, 1:43:40 PM Β· Difficulty 10.6371 Β· 4,978,961 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c48feae4e572b00a37f80f2a6822edb87748c11b8ac10a1269e8077fe4725a8
View on Chainz β†—

Height

#1,853,195

Difficulty

10.637090

Transactions

1

Size

243 B

Version

2

Bits

0aa31859

Nonce

132,121,724

Timestamp

11/17/2016, 1:43:40 PM

Confirmations

4,978,961

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

73402a3b57254224b5051e8856865d25334729291ee66841efec83c395c428fe
Transactions (1)
Coinbase73402a3b572542…ec83c395c428fe
1 in β†’ 2 out8.8200 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

3.964 Γ— 10⁹⁢(97-digit number)
39646842311541548056…99793083244262223359
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
3.964 Γ— 10⁹⁢(97-digit number)
39646842311541548056…99793083244262223359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.964 Γ— 10⁹⁢(97-digit number)
39646842311541548056…99793083244262223361
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
7.929 Γ— 10⁹⁢(97-digit number)
79293684623083096112…99586166488524446719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.929 Γ— 10⁹⁢(97-digit number)
79293684623083096112…99586166488524446721
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
1.585 Γ— 10⁹⁷(98-digit number)
15858736924616619222…99172332977048893439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.585 Γ— 10⁹⁷(98-digit number)
15858736924616619222…99172332977048893441
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
3.171 Γ— 10⁹⁷(98-digit number)
31717473849233238445…98344665954097786879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.171 Γ— 10⁹⁷(98-digit number)
31717473849233238445…98344665954097786881
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
6.343 Γ— 10⁹⁷(98-digit number)
63434947698466476890…96689331908195573759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.343 Γ— 10⁹⁷(98-digit number)
63434947698466476890…96689331908195573761
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
1.268 Γ— 10⁹⁸(99-digit number)
12686989539693295378…93378663816391147519
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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