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Block #1,105,761

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/15/2015, 3:58:50 AM Β· Difficulty 10.7870 Β· 5,705,194 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4fd3b785a05979c77b8c8329dd14383838f8a3e16ef4a703df8e35c0a72dbbd6
View on Chainz β†—

Height

#1,105,761

Difficulty

10.786951

Transactions

2

Size

19.35 KB

Version

2

Bits

0ac975a2

Nonce

777,647,881

Timestamp

6/15/2015, 3:58:50 AM

Confirmations

5,705,194

Mined by

⛏️ P2SHAZQ6vdZV2bZGsx5UpbtLxUhUAhKywCrL3y

Merkle Root

df2e4739772b71e8df8b093c407f177123c4a2269f9ed700370b2e8964e06f6e
Transactions (2)
Coinbase11070517b5d712…ec48654b3efb6c
1 in β†’ 1 out8.9000 XPM110 B
AZQ6vdZV…KywCrL3y
2a850bd135be02…9be560c68ae767
132 in β†’ 2 out396000.0107 XPM19.15 KB
ASxDRQ4S…LQLqimiNAMb2RL9J…zTbGj3be
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.

1.245 Γ— 10⁹⁡(96-digit number)
12453293412218266042…44002407747931156479
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
1.245 Γ— 10⁹⁡(96-digit number)
12453293412218266042…44002407747931156479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.245 Γ— 10⁹⁡(96-digit number)
12453293412218266042…44002407747931156481
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
2.490 Γ— 10⁹⁡(96-digit number)
24906586824436532084…88004815495862312959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.490 Γ— 10⁹⁡(96-digit number)
24906586824436532084…88004815495862312961
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
4.981 Γ— 10⁹⁡(96-digit number)
49813173648873064169…76009630991724625919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.981 Γ— 10⁹⁡(96-digit number)
49813173648873064169…76009630991724625921
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
9.962 Γ— 10⁹⁡(96-digit number)
99626347297746128339…52019261983449251839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.962 Γ— 10⁹⁡(96-digit number)
99626347297746128339…52019261983449251841
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
1.992 Γ— 10⁹⁢(97-digit number)
19925269459549225667…04038523966898503679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.992 Γ— 10⁹⁢(97-digit number)
19925269459549225667…04038523966898503681
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:57,731,740 XPMΒ·at block #6,810,954 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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