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Block #303,728

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/10/2013, 1:06:39 PM Β· Difficulty 9.9931 Β· 6,499,737 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6a140bee03b80d7d138762bc3bf5f2863b8c204bdcff97577e654314a10e991a
View on Chainz β†—

Height

#303,728

Difficulty

9.993104

Transactions

1

Size

1.01 KB

Version

2

Bits

09fe3c17

Nonce

202,955

Timestamp

12/10/2013, 1:06:39 PM

Confirmations

6,499,737

Mined by

⛏️ paRAWZd1qVJsLEYJ7QkpZDB3cXqFz9pj9yfPa

Merkle Root

f2e5b50cbcb570eef7133820cb7fad0adbce0eedde4f70a677693b54b2341a82
Transactions (1)
Coinbasef2e5b50cbcb570…693b54b2341a82
1 in β†’ 26 out10.0000 XPM947 B
AWZd1qVJ…9pj9yfPaAHyYT7So…agW8WWrgAZ2pPuKg…95SN2Yr7AG5YAjec…VhA4Aeh1AP72ZF1f…K2ngR7CZ
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.

2.708 Γ— 10⁹⁴(95-digit number)
27080291444379464715…65419962309591496319
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
2.708 Γ— 10⁹⁴(95-digit number)
27080291444379464715…65419962309591496319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.708 Γ— 10⁹⁴(95-digit number)
27080291444379464715…65419962309591496321
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
5.416 Γ— 10⁹⁴(95-digit number)
54160582888758929430…30839924619182992639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.416 Γ— 10⁹⁴(95-digit number)
54160582888758929430…30839924619182992641
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
1.083 Γ— 10⁹⁡(96-digit number)
10832116577751785886…61679849238365985279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.083 Γ— 10⁹⁡(96-digit number)
10832116577751785886…61679849238365985281
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
2.166 Γ— 10⁹⁡(96-digit number)
21664233155503571772…23359698476731970559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.166 Γ— 10⁹⁡(96-digit number)
21664233155503571772…23359698476731970561
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
4.332 Γ— 10⁹⁡(96-digit number)
43328466311007143544…46719396953463941119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.332 Γ— 10⁹⁡(96-digit number)
43328466311007143544…46719396953463941121
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:57,671,748 XPMΒ·at block #6,803,464 Β· updates every 60s
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