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Block #225,874

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/24/2013, 7:51:07 PM Β· Difficulty 9.9362 Β· 6,586,353 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9aa6724f0fae4ba23dc4f233d7222da9c9f88bf3bee2ecfe8f27c7247e52b99b
View on Chainz β†—

Height

#225,874

Difficulty

9.936162

Transactions

1

Size

197 B

Version

2

Bits

09efa84e

Nonce

22,045

Timestamp

10/24/2013, 7:51:07 PM

Confirmations

6,586,353

Mined by

⛏️ P2SHAMDDjcKidTR7e5DmAbqsZdJTifMcrtk5gH

Merkle Root

9a23c9fece2f87c5dfa9193a47525923b9ebeeb4ae8ec9f4b4f01019869faf54
Transactions (1)
Coinbase9a23c9fece2f87…f01019869faf54
1 in β†’ 1 out10.1100 XPM109 B
AMDDjcKi…Mcrtk5gH
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.

2.847 Γ— 10⁸⁹(90-digit number)
28475378642814126108…18187186098356820479
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
2.847 Γ— 10⁸⁹(90-digit number)
28475378642814126108…18187186098356820479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.847 Γ— 10⁸⁹(90-digit number)
28475378642814126108…18187186098356820481
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
5.695 Γ— 10⁸⁹(90-digit number)
56950757285628252216…36374372196713640959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.695 Γ— 10⁸⁹(90-digit number)
56950757285628252216…36374372196713640961
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
1.139 Γ— 10⁹⁰(91-digit number)
11390151457125650443…72748744393427281919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.139 Γ— 10⁹⁰(91-digit number)
11390151457125650443…72748744393427281921
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
2.278 Γ— 10⁹⁰(91-digit number)
22780302914251300886…45497488786854563839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.278 Γ— 10⁹⁰(91-digit number)
22780302914251300886…45497488786854563841
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
4.556 Γ— 10⁹⁰(91-digit number)
45560605828502601773…90994977573709127679
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:57,741,831 XPMΒ·at block #6,812,226 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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