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Block #225,074

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/24/2013, 5:55:14 AM Β· Difficulty 9.9366 Β· 6,618,185 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
919da668e3aebd87ff918475e5136bd84094971adee1cad22fdd8554b3ee4d4d
View on Chainz β†—

Height

#225,074

Difficulty

9.936595

Transactions

1

Size

206 B

Version

2

Bits

09efc4ab

Nonce

233,011

Timestamp

10/24/2013, 5:55:14 AM

Confirmations

6,618,185

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

800015165eee02df52749677f05241c01cc85a5dfef600e44ad0608100134193
Transactions (1)
Coinbase800015165eee02…d0608100134193
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

3.451 Γ— 10⁹⁴(95-digit number)
34511485721363033590…49650342517993569999
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
3.451 Γ— 10⁹⁴(95-digit number)
34511485721363033590…49650342517993569999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.451 Γ— 10⁹⁴(95-digit number)
34511485721363033590…49650342517993570001
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
6.902 Γ— 10⁹⁴(95-digit number)
69022971442726067181…99300685035987139999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.902 Γ— 10⁹⁴(95-digit number)
69022971442726067181…99300685035987140001
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
1.380 Γ— 10⁹⁡(96-digit number)
13804594288545213436…98601370071974279999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.380 Γ— 10⁹⁡(96-digit number)
13804594288545213436…98601370071974280001
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
2.760 Γ— 10⁹⁡(96-digit number)
27609188577090426872…97202740143948559999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.760 Γ— 10⁹⁡(96-digit number)
27609188577090426872…97202740143948560001
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
5.521 Γ— 10⁹⁡(96-digit number)
55218377154180853744…94405480287897119999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.521 Γ— 10⁹⁡(96-digit number)
55218377154180853744…94405480287897120001
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
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