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Block #1,162,855

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2015, 5:45:18 PM Β· Difficulty 10.9352 Β· 5,642,278 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ed3b4bcc6822f6478bd1f30189b6c6a4d2b87b46dbfd051ecdc27a96f7fa00d
View on Chainz β†—

Height

#1,162,855

Difficulty

10.935180

Transactions

2

Size

8.36 KB

Version

2

Bits

0aef67f8

Nonce

104,685,917

Timestamp

7/20/2015, 5:45:18 PM

Confirmations

5,642,278

Mined by

⛏️ P2SHAQ5jqdr8PYEVPpp6vpG9AUX5EyXXF575EU

Merkle Root

fcbc2cd30bc5f936657f6eb262db784f931d5d9d82a4d6533493d1a805d8d8e3
Transactions (2)
Coinbase0d4be0e06cc401…d4300bb2965319
1 in β†’ 1 out8.5400 XPM110 B
AQ5jqdr8…XXF575EU
71c2cdeb705916…a7305f54dfd94a
56 in β†’ 2 out575.8168 XPM8.16 KB
AQHE5e6H…xDwU3vYUAGmzWPUs…7Z2s5NZV
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.

2.279 Γ— 10⁹⁸(99-digit number)
22792402473539756434…00142675363243950079
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
2.279 Γ— 10⁹⁸(99-digit number)
22792402473539756434…00142675363243950079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.279 Γ— 10⁹⁸(99-digit number)
22792402473539756434…00142675363243950081
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
4.558 Γ— 10⁹⁸(99-digit number)
45584804947079512869…00285350726487900159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.558 Γ— 10⁹⁸(99-digit number)
45584804947079512869…00285350726487900161
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
9.116 Γ— 10⁹⁸(99-digit number)
91169609894159025739…00570701452975800319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.116 Γ— 10⁹⁸(99-digit number)
91169609894159025739…00570701452975800321
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
1.823 Γ— 10⁹⁹(100-digit number)
18233921978831805147…01141402905951600639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.823 Γ— 10⁹⁹(100-digit number)
18233921978831805147…01141402905951600641
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
3.646 Γ— 10⁹⁹(100-digit number)
36467843957663610295…02282805811903201279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.646 Γ— 10⁹⁹(100-digit number)
36467843957663610295…02282805811903201281
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:57,685,128 XPMΒ·at block #6,805,132 Β· updates every 60s
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