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Block #2,634,780

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 12:38:42 AM Β· Difficulty 11.2692 Β· 4,202,089 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca769c0f5aadb8c5100de80e47ce070d19bf0eb58ec053c3771b16f1eb8a245f
View on Chainz β†—

Height

#2,634,780

Difficulty

11.269173

Transactions

1

Size

200 B

Version

2

Bits

0b44e87f

Nonce

137,121,053

Timestamp

4/29/2018, 12:38:42 AM

Confirmations

4,202,089

Mined by

⛏️ P2SHAaSrKR6Ew7pijamAvGCWC6zxchQvmpyqn6

Merkle Root

c8f5fea2266fb5f94326ee9c4b1fd5922ead156026c9144b2174a4b5f01e78f6
Transactions (1)
Coinbasec8f5fea2266fb5…74a4b5f01e78f6
1 in β†’ 1 out7.8600 XPM110 B
AaSrKR6E…Qvmpyqn6
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.

3.319 Γ— 10⁹⁡(96-digit number)
33199953051998656775…99943253998845758399
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
3.319 Γ— 10⁹⁡(96-digit number)
33199953051998656775…99943253998845758399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.319 Γ— 10⁹⁡(96-digit number)
33199953051998656775…99943253998845758401
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
6.639 Γ— 10⁹⁡(96-digit number)
66399906103997313550…99886507997691516799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.639 Γ— 10⁹⁡(96-digit number)
66399906103997313550…99886507997691516801
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
1.327 Γ— 10⁹⁢(97-digit number)
13279981220799462710…99773015995383033599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.327 Γ— 10⁹⁢(97-digit number)
13279981220799462710…99773015995383033601
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
2.655 Γ— 10⁹⁢(97-digit number)
26559962441598925420…99546031990766067199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.655 Γ— 10⁹⁢(97-digit number)
26559962441598925420…99546031990766067201
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
5.311 Γ— 10⁹⁢(97-digit number)
53119924883197850840…99092063981532134399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.311 Γ— 10⁹⁢(97-digit number)
53119924883197850840…99092063981532134401
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
1.062 Γ— 10⁹⁷(98-digit number)
10623984976639570168…98184127963064268799
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.062 Γ— 10⁹⁷(98-digit number)
10623984976639570168…98184127963064268801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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
Circulating Supply:57,939,242 XPMΒ·at block #6,836,868 Β· updates every 60s
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