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Block #205,679

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/12/2013, 7:36:48 AM Β· Difficulty 9.9002 Β· 6,591,205 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
15c170cdd05f861317b811b058c34c9e0da9e828e121721c12e10a960a40fbe7
View on Chainz β†—

Height

#205,679

Difficulty

9.900157

Transactions

1

Size

199 B

Version

2

Bits

09e670b2

Nonce

130,881

Timestamp

10/12/2013, 7:36:48 AM

Confirmations

6,591,205

Mined by

⛏️ P2SHANGBbZBtZNuys6AnqQKZZta4BvV1FiVbe4

Merkle Root

6572d1119dafbc1ea44a61226a7e687ac4f14a6223ef9501a8ffdf513a54b477
Transactions (1)
Coinbase6572d1119dafbc…ffdf513a54b477
1 in β†’ 1 out10.1900 XPM109 B
ANGBbZBt…V1FiVbe4
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.

2.083 Γ— 10⁹⁡(96-digit number)
20831671813342875914…95083845996806206719
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
2.083 Γ— 10⁹⁡(96-digit number)
20831671813342875914…95083845996806206719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.083 Γ— 10⁹⁡(96-digit number)
20831671813342875914…95083845996806206721
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
4.166 Γ— 10⁹⁡(96-digit number)
41663343626685751828…90167691993612413439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.166 Γ— 10⁹⁡(96-digit number)
41663343626685751828…90167691993612413441
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
8.332 Γ— 10⁹⁡(96-digit number)
83326687253371503657…80335383987224826879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.332 Γ— 10⁹⁡(96-digit number)
83326687253371503657…80335383987224826881
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
1.666 Γ— 10⁹⁢(97-digit number)
16665337450674300731…60670767974449653759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.666 Γ— 10⁹⁢(97-digit number)
16665337450674300731…60670767974449653761
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
3.333 Γ— 10⁹⁢(97-digit number)
33330674901348601462…21341535948899307519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.333 Γ— 10⁹⁢(97-digit number)
33330674901348601462…21341535948899307521
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:57,619,089 XPMΒ·at block #6,796,883 Β· updates every 60s
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