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Block #211,242

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/15/2013, 3:00:05 PM Β· Difficulty 9.9151 Β· 6,583,930 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2c62721d96093d62528808a31ad8bc0e86abb17c7cbd5c3ea2e702fa7f087afa
View on Chainz β†—

Height

#211,242

Difficulty

9.915099

Transactions

2

Size

1.14 KB

Version

2

Bits

09ea43ed

Nonce

3,189

Timestamp

10/15/2013, 3:00:05 PM

Confirmations

6,583,930

Mined by

⛏️ P2SHAeoUViYcgPUbgiXwhWb8MJT88CmMhwZhvj

Merkle Root

b2b4d08fe12da6dd06695880d3d2f6cc337e7c5cc7bba7442f7682cbf278907f
Transactions (2)
Coinbase1b31b989e17778…9d5565ef474b99
1 in β†’ 1 out10.1700 XPM109 B
AeoUViYc…mMhwZhvj
81a39671951b34…17e4077b0bbc1e
6 in β†’ 2 out2400.0862 XPM968 B
AJm1dWJ4…2QRNNjdvAM4M1K2v…H8xfBx5T
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.

3.009 Γ— 10⁹⁡(96-digit number)
30090880263246929159…79446303380360793879
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
3.009 Γ— 10⁹⁡(96-digit number)
30090880263246929159…79446303380360793879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.009 Γ— 10⁹⁡(96-digit number)
30090880263246929159…79446303380360793881
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
6.018 Γ— 10⁹⁡(96-digit number)
60181760526493858318…58892606760721587759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.018 Γ— 10⁹⁡(96-digit number)
60181760526493858318…58892606760721587761
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
1.203 Γ— 10⁹⁢(97-digit number)
12036352105298771663…17785213521443175519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.203 Γ— 10⁹⁢(97-digit number)
12036352105298771663…17785213521443175521
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
2.407 Γ— 10⁹⁢(97-digit number)
24072704210597543327…35570427042886351039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.407 Γ— 10⁹⁢(97-digit number)
24072704210597543327…35570427042886351041
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
4.814 Γ— 10⁹⁢(97-digit number)
48145408421195086654…71140854085772702079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.814 Γ— 10⁹⁢(97-digit number)
48145408421195086654…71140854085772702081
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:57,605,422 XPMΒ·at block #6,795,171 Β· updates every 60s
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