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Block #225,778

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/24/2013, 6:15:44 PM Β· Difficulty 9.9362 Β· 6,585,292 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6250a89258d7174762238fbced074bf5f3dbc10083504280d593995d04e335ea
View on Chainz β†—

Height

#225,778

Difficulty

9.936154

Transactions

1

Size

199 B

Version

2

Bits

09efa7cc

Nonce

138,109

Timestamp

10/24/2013, 6:15:44 PM

Confirmations

6,585,292

Mined by

⛏️ P2SHAHnC2vHTnpRWffuNbHGv3Mh3M9SjbyyVBp

Merkle Root

d1d089b6e476f823ee8af6648d455aa465a179491254196685769148d11ea638
Transactions (1)
Coinbased1d089b6e476f8…769148d11ea638
1 in β†’ 1 out10.1100 XPM109 B
AHnC2vHT…SjbyyVBp
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.

3.840 Γ— 10⁹³(94-digit number)
38405265870414864306…39752513524666111999
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
3.840 Γ— 10⁹³(94-digit number)
38405265870414864306…39752513524666111999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.840 Γ— 10⁹³(94-digit number)
38405265870414864306…39752513524666112001
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
7.681 Γ— 10⁹³(94-digit number)
76810531740829728613…79505027049332223999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.681 Γ— 10⁹³(94-digit number)
76810531740829728613…79505027049332224001
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
1.536 Γ— 10⁹⁴(95-digit number)
15362106348165945722…59010054098664447999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.536 Γ— 10⁹⁴(95-digit number)
15362106348165945722…59010054098664448001
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
3.072 Γ— 10⁹⁴(95-digit number)
30724212696331891445…18020108197328895999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.072 Γ— 10⁹⁴(95-digit number)
30724212696331891445…18020108197328896001
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
6.144 Γ— 10⁹⁴(95-digit number)
61448425392663782891…36040216394657791999
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:57,732,667 XPMΒ·at block #6,811,069 Β· updates every 60s
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