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Block #1,109,226

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/16/2015, 6:18:22 AM Β· Difficulty 10.8535 Β· 5,697,898 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7e842d8fa523ab48212660ae2a3d47cc3a893c57232ad69db486f20a7aa70748
View on Chainz β†—

Height

#1,109,226

Difficulty

10.853522

Transactions

2

Size

425 B

Version

2

Bits

0ada8065

Nonce

706,200,205

Timestamp

6/16/2015, 6:18:22 AM

Confirmations

5,697,898

Mined by

⛏️ P2SHAaZX7Vg9yFrtwcgF6MUymFDVJ6cPnLs9Jo

Merkle Root

b2914fffd7b7dc1fa819029c0145ca8cdf5a7d115b03b7e2761bff9feecdb13c
Transactions (2)
Coinbase019b46d10a0dfe…d33084f3815d9b
1 in β†’ 1 out8.4900 XPM109 B
AaZX7Vg9…cPnLs9Jo
a4e054a57058b8…40d37d80c47488
1 in β†’ 2 out1.2047 XPM226 B
AVYjNJEW…jTeas9v4Ad2QVk8j…7wqy2uYk
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.

3.723 Γ— 10⁹⁡(96-digit number)
37231479186861447289…90769789948881383679
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
3.723 Γ— 10⁹⁡(96-digit number)
37231479186861447289…90769789948881383679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.723 Γ— 10⁹⁡(96-digit number)
37231479186861447289…90769789948881383681
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
7.446 Γ— 10⁹⁡(96-digit number)
74462958373722894579…81539579897762767359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.446 Γ— 10⁹⁡(96-digit number)
74462958373722894579…81539579897762767361
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
1.489 Γ— 10⁹⁢(97-digit number)
14892591674744578915…63079159795525534719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.489 Γ— 10⁹⁢(97-digit number)
14892591674744578915…63079159795525534721
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
2.978 Γ— 10⁹⁢(97-digit number)
29785183349489157831…26158319591051069439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.978 Γ— 10⁹⁢(97-digit number)
29785183349489157831…26158319591051069441
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
5.957 Γ— 10⁹⁢(97-digit number)
59570366698978315663…52316639182102138879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.957 Γ— 10⁹⁢(97-digit number)
59570366698978315663…52316639182102138881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.191 Γ— 10⁹⁷(98-digit number)
11914073339795663132…04633278364204277759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,701,095 XPMΒ·at block #6,807,123 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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