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Block #3,048,995

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/11/2019, 11:37:49 PM Β· Difficulty 10.9961 Β· 3,792,492 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c0148aa9482131c2f2f0535b120ece51e41078aa27b56fcafee82c274a1d422
View on Chainz β†—

Height

#3,048,995

Difficulty

10.996080

Transactions

1

Size

201 B

Version

2

Bits

0afeff17

Nonce

234,929,331

Timestamp

2/11/2019, 11:37:49 PM

Confirmations

3,792,492

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

ab6c59c4b872845c395e3baa1b0ef1a45f87b1b7a33f4558b3bebb19a3cbf0f0
Transactions (1)
Coinbaseab6c59c4b87284…bebb19a3cbf0f0
1 in β†’ 1 out8.2600 XPM110 B
AbXwmGxD…4XXYP765
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.

5.360 Γ— 10⁹⁷(98-digit number)
53603056601478545092…20254677543163135999
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
5.360 Γ— 10⁹⁷(98-digit number)
53603056601478545092…20254677543163135999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.360 Γ— 10⁹⁷(98-digit number)
53603056601478545092…20254677543163136001
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
1.072 Γ— 10⁹⁸(99-digit number)
10720611320295709018…40509355086326271999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.072 Γ— 10⁹⁸(99-digit number)
10720611320295709018…40509355086326272001
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
2.144 Γ— 10⁹⁸(99-digit number)
21441222640591418037…81018710172652543999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.144 Γ— 10⁹⁸(99-digit number)
21441222640591418037…81018710172652544001
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
4.288 Γ— 10⁹⁸(99-digit number)
42882445281182836074…62037420345305087999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.288 Γ— 10⁹⁸(99-digit number)
42882445281182836074…62037420345305088001
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
8.576 Γ— 10⁹⁸(99-digit number)
85764890562365672148…24074840690610175999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.576 Γ— 10⁹⁸(99-digit number)
85764890562365672148…24074840690610176001
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
1.715 Γ— 10⁹⁹(100-digit number)
17152978112473134429…48149681381220351999
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:57,976,272 XPMΒ·at block #6,841,486 Β· updates every 60s
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