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Block #3,341,339

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2019, 12:50:52 AM Β· Difficulty 11.0031 Β· 3,498,437 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cd79fb2aa33e38e631565d90901fca455aabe94139a53a1cf4f918a83783eac3
View on Chainz β†—

Height

#3,341,339

Difficulty

11.003058

Transactions

2

Size

722 B

Version

2

Bits

0b00c866

Nonce

1,563,287,372

Timestamp

9/5/2019, 12:50:52 AM

Confirmations

3,498,437

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

07222ce562190748918c24ed3a7fe5968262692127ac48669e01081b19c7305e
Transactions (2)
Coinbasebb90897569f4fb…1bf9e6378f102e
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
e429dda20f49ee…c4bb19a4908f94
3 in β†’ 2 out36.3645 XPM521 B
AQx3LLNU…JqVD6HwpAeTHTL7A…vT1872bk
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.

3.740 Γ— 10⁹⁢(97-digit number)
37405274764536893531…16062703021927403519
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
3.740 Γ— 10⁹⁢(97-digit number)
37405274764536893531…16062703021927403519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.740 Γ— 10⁹⁢(97-digit number)
37405274764536893531…16062703021927403521
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
7.481 Γ— 10⁹⁢(97-digit number)
74810549529073787062…32125406043854807039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.481 Γ— 10⁹⁢(97-digit number)
74810549529073787062…32125406043854807041
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
1.496 Γ— 10⁹⁷(98-digit number)
14962109905814757412…64250812087709614079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.496 Γ— 10⁹⁷(98-digit number)
14962109905814757412…64250812087709614081
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
2.992 Γ— 10⁹⁷(98-digit number)
29924219811629514825…28501624175419228159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.992 Γ— 10⁹⁷(98-digit number)
29924219811629514825…28501624175419228161
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
5.984 Γ— 10⁹⁷(98-digit number)
59848439623259029650…57003248350838456319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.984 Γ— 10⁹⁷(98-digit number)
59848439623259029650…57003248350838456321
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
1.196 Γ— 10⁹⁸(99-digit number)
11969687924651805930…14006496701676912639
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:57,962,498 XPMΒ·at block #6,839,775 Β· updates every 60s
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