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Block #221,089

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/21/2013, 9:30:05 AM Β· Difficulty 9.9379 Β· 6,594,901 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
baa0a4e194eaadf0a16994ed4f1b01539603992f60c7b7a05fb52fd31b99cd0a
View on Chainz β†—

Height

#221,089

Difficulty

9.937918

Transactions

1

Size

199 B

Version

2

Bits

09f01b65

Nonce

9,808

Timestamp

10/21/2013, 9:30:05 AM

Confirmations

6,594,901

Mined by

⛏️ P2SHATRnMoWiPfLU4bA2TUCHsxS8iKZP2o2dcV

Merkle Root

9f67caec09385078dae8bdc839185349f05b364f197064f4cfe281b483296d48
Transactions (1)
Coinbase9f67caec093850…e281b483296d48
1 in β†’ 1 out10.1100 XPM109 B
ATRnMoWi…ZP2o2dcV
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.

8.786 Γ— 10⁹³(94-digit number)
87865580064326692923…26230115947719521279
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
8.786 Γ— 10⁹³(94-digit number)
87865580064326692923…26230115947719521279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.786 Γ— 10⁹³(94-digit number)
87865580064326692923…26230115947719521281
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
1.757 Γ— 10⁹⁴(95-digit number)
17573116012865338584…52460231895439042559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.757 Γ— 10⁹⁴(95-digit number)
17573116012865338584…52460231895439042561
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
3.514 Γ— 10⁹⁴(95-digit number)
35146232025730677169…04920463790878085119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.514 Γ— 10⁹⁴(95-digit number)
35146232025730677169…04920463790878085121
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
7.029 Γ— 10⁹⁴(95-digit number)
70292464051461354339…09840927581756170239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.029 Γ— 10⁹⁴(95-digit number)
70292464051461354339…09840927581756170241
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
1.405 Γ— 10⁹⁡(96-digit number)
14058492810292270867…19681855163512340479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,772,034 XPMΒ·at block #6,815,989 Β· updates every 60s
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