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Block #2,641,333

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 7:45:28 AM Β· Difficulty 11.6163 Β· 4,195,586 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bc0f0a754637524b55036b3d445b4b486c99d40b6a13250d7f3cd372d0c5b1df
View on Chainz β†—

Height

#2,641,333

Difficulty

11.616341

Transactions

1

Size

199 B

Version

2

Bits

0b9dc88b

Nonce

135,073,575

Timestamp

5/1/2018, 7:45:28 AM

Confirmations

4,195,586

Mined by

⛏️ P2SHAP1EjhwQh56t2uppqBGQzWYYvQvrPa4M91

Merkle Root

e7b08dcdf1c94d400e3a37bc8df022b11ad06f3c9ad411bcefa1623a771012cf
Transactions (1)
Coinbasee7b08dcdf1c94d…a1623a771012cf
1 in β†’ 1 out7.4000 XPM110 B
AP1EjhwQ…vrPa4M91
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.

1.852 Γ— 10⁹²(93-digit number)
18524794825967811783…55714227252951821439
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
1.852 Γ— 10⁹²(93-digit number)
18524794825967811783…55714227252951821439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.852 Γ— 10⁹²(93-digit number)
18524794825967811783…55714227252951821441
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
3.704 Γ— 10⁹²(93-digit number)
37049589651935623567…11428454505903642879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.704 Γ— 10⁹²(93-digit number)
37049589651935623567…11428454505903642881
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
7.409 Γ— 10⁹²(93-digit number)
74099179303871247134…22856909011807285759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.409 Γ— 10⁹²(93-digit number)
74099179303871247134…22856909011807285761
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
1.481 Γ— 10⁹³(94-digit number)
14819835860774249426…45713818023614571519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.481 Γ— 10⁹³(94-digit number)
14819835860774249426…45713818023614571521
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
2.963 Γ— 10⁹³(94-digit number)
29639671721548498853…91427636047229143039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.963 Γ— 10⁹³(94-digit number)
29639671721548498853…91427636047229143041
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
5.927 Γ— 10⁹³(94-digit number)
59279343443096997707…82855272094458286079
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:57,939,646 XPMΒ·at block #6,836,918 Β· updates every 60s
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