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Block #2,662,113

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/15/2018, 1:02:04 PM Β· Difficulty 11.6396 Β· 4,171,352 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a215896344ca6ad5558143796cff9c52b50596f2416c75ced463c4c5e3011013
View on Chainz β†—

Height

#2,662,113

Difficulty

11.639648

Transactions

2

Size

1017 B

Version

2

Bits

0ba3c000

Nonce

211,564,657

Timestamp

5/15/2018, 1:02:04 PM

Confirmations

4,171,352

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

af7ce585c06ff393d0be317335fd71fc727a6d9045143ce7e940a284503df372
Transactions (2)
Coinbase9805a41bfd160a…e32a37803a93ce
1 in β†’ 1 out7.3800 XPM110 B
Adqah8zh…1WwoHJ9t
1d98142c68de6c…7e72520b5fb739
5 in β†’ 2 out10500.0100 XPM816 B
ANV3WZ1g…j2nrtPwLAYroy9Y9…ARnBPcoG
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.

3.921 Γ— 10⁹⁷(98-digit number)
39214037166706289967…85000421934649507839
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
3.921 Γ— 10⁹⁷(98-digit number)
39214037166706289967…85000421934649507839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.921 Γ— 10⁹⁷(98-digit number)
39214037166706289967…85000421934649507841
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
7.842 Γ— 10⁹⁷(98-digit number)
78428074333412579934…70000843869299015679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.842 Γ— 10⁹⁷(98-digit number)
78428074333412579934…70000843869299015681
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
1.568 Γ— 10⁹⁸(99-digit number)
15685614866682515986…40001687738598031359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.568 Γ— 10⁹⁸(99-digit number)
15685614866682515986…40001687738598031361
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
3.137 Γ— 10⁹⁸(99-digit number)
31371229733365031973…80003375477196062719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.137 Γ— 10⁹⁸(99-digit number)
31371229733365031973…80003375477196062721
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
6.274 Γ— 10⁹⁸(99-digit number)
62742459466730063947…60006750954392125439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.274 Γ— 10⁹⁸(99-digit number)
62742459466730063947…60006750954392125441
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
1.254 Γ— 10⁹⁹(100-digit number)
12548491893346012789…20013501908784250879
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:57,911,921 XPMΒ·at block #6,833,464 Β· updates every 60s
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