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Block #1,589,190

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/17/2016, 11:05:09 PM Β· Difficulty 10.6520 Β· 5,250,189 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a96c27880e8e8fe1a5b1615209bf9840877e6bb939c4758910bf6c7bfe665f66
View on Chainz β†—

Height

#1,589,190

Difficulty

10.652013

Transactions

1

Size

242 B

Version

2

Bits

0aa6ea53

Nonce

221,151,216

Timestamp

5/17/2016, 11:05:09 PM

Confirmations

5,250,189

Mined by

⛏️ P2SHAJgZBh3x4MUdHjG3qq81iJgboZ9DpUcwi5

Merkle Root

914fc45b6e05a12cf7cf16a415cb6daa0d94535340a80fa1404ddf57714bbd19
Transactions (1)
Coinbase914fc45b6e05a1…4ddf57714bbd19
1 in β†’ 2 out8.8000 XPM152 B
AJgZBh3x…9DpUcwi5ALPu3s2c…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.

1.765 Γ— 10⁹⁡(96-digit number)
17654300465798281964…51295001651636973199
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
1.765 Γ— 10⁹⁡(96-digit number)
17654300465798281964…51295001651636973199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.765 Γ— 10⁹⁡(96-digit number)
17654300465798281964…51295001651636973201
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
3.530 Γ— 10⁹⁡(96-digit number)
35308600931596563928…02590003303273946399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.530 Γ— 10⁹⁡(96-digit number)
35308600931596563928…02590003303273946401
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
7.061 Γ— 10⁹⁡(96-digit number)
70617201863193127856…05180006606547892799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.061 Γ— 10⁹⁡(96-digit number)
70617201863193127856…05180006606547892801
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
1.412 Γ— 10⁹⁢(97-digit number)
14123440372638625571…10360013213095785599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.412 Γ— 10⁹⁢(97-digit number)
14123440372638625571…10360013213095785601
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
2.824 Γ— 10⁹⁢(97-digit number)
28246880745277251142…20720026426191571199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.824 Γ— 10⁹⁢(97-digit number)
28246880745277251142…20720026426191571201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,959,315 XPMΒ·at block #6,839,378 Β· updates every 60s
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