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Block #43,861

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 10:06:41 PM Β· Difficulty 8.6863 Β· 6,759,210 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9a4ee9009424ea13da42ec2ee9680a4e52b41af76ec5bae619184a7793b2716c
View on Chainz β†—

Height

#43,861

Difficulty

8.686345

Transactions

1

Size

204 B

Version

2

Bits

08afb453

Nonce

648

Timestamp

7/14/2013, 10:06:41 PM

Confirmations

6,759,210

Mined by

⛏️ P2SHAWgEG14hmNKcJW2BYiFzGVLyavaBpFjLKE

Merkle Root

556f2be6a1e4ef2048b3e2d5d25e75835201a91b24651d627b8b467ca992dc43
Transactions (1)
Coinbase556f2be6a1e4ef…8b467ca992dc43
1 in β†’ 1 out13.2400 XPM110 B
AWgEG14h…aBpFjLKE
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.

5.582 Γ— 10¹⁰³(104-digit number)
55824521342584026108…70630639304512498449
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
5.582 Γ— 10¹⁰³(104-digit number)
55824521342584026108…70630639304512498449
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.582 Γ— 10¹⁰³(104-digit number)
55824521342584026108…70630639304512498451
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
1.116 Γ— 10¹⁰⁴(105-digit number)
11164904268516805221…41261278609024996899
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.116 Γ— 10¹⁰⁴(105-digit number)
11164904268516805221…41261278609024996901
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
2.232 Γ— 10¹⁰⁴(105-digit number)
22329808537033610443…82522557218049993799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.232 Γ— 10¹⁰⁴(105-digit number)
22329808537033610443…82522557218049993801
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
4.465 Γ— 10¹⁰⁴(105-digit number)
44659617074067220886…65045114436099987599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.465 Γ— 10¹⁰⁴(105-digit number)
44659617074067220886…65045114436099987601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,668,597 XPMΒ·at block #6,803,070 Β· updates every 60s
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