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Block #2,819,621

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/1/2018, 7:47:57 AM Β· Difficulty 11.7012 Β· 4,022,812 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1ca8fb538f744d845d2232b6199fd2ac5c59c1c7a7fd928473a6641c5c93ad8c
View on Chainz β†—

Height

#2,819,621

Difficulty

11.701178

Transactions

2

Size

2.44 KB

Version

2

Bits

0bb38061

Nonce

194,764,164

Timestamp

9/1/2018, 7:47:57 AM

Confirmations

4,022,812

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

fd9672ca5db18255e843d879a67d81deb07f3010f13a0bc19aabc2f263869d6b
Transactions (2)
Coinbase438e1acd26edad…a28b9c44ee0fb8
1 in β†’ 1 out7.3200 XPM110 B
AZtxQr2F…7grUWrUz
1a79467c30d621…c68ccb7ec97624
15 in β†’ 2 out140.0800 XPM2.25 KB
ATBBzUDp…myR6ZS42ALh5G3Np…6TsNC2wj
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.

2.740 Γ— 10⁹⁡(96-digit number)
27403740005944843651…23409259513527805439
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
2.740 Γ— 10⁹⁡(96-digit number)
27403740005944843651…23409259513527805439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.740 Γ— 10⁹⁡(96-digit number)
27403740005944843651…23409259513527805441
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
5.480 Γ— 10⁹⁡(96-digit number)
54807480011889687302…46818519027055610879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.480 Γ— 10⁹⁡(96-digit number)
54807480011889687302…46818519027055610881
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
1.096 Γ— 10⁹⁢(97-digit number)
10961496002377937460…93637038054111221759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.096 Γ— 10⁹⁢(97-digit number)
10961496002377937460…93637038054111221761
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
2.192 Γ— 10⁹⁢(97-digit number)
21922992004755874920…87274076108222443519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.192 Γ— 10⁹⁢(97-digit number)
21922992004755874920…87274076108222443521
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
4.384 Γ— 10⁹⁢(97-digit number)
43845984009511749841…74548152216444887039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.384 Γ— 10⁹⁢(97-digit number)
43845984009511749841…74548152216444887041
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
8.769 Γ— 10⁹⁢(97-digit number)
87691968019023499683…49096304432889774079
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:57,983,879 XPMΒ·at block #6,842,432 Β· updates every 60s
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