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Block #2,119,851

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/16/2017, 11:50:04 PM Β· Difficulty 10.9116 Β· 4,712,831 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
514ebc1e2b97447a169fcf97a11f991b7cc320f66ef15b88e0c15039ce39b25f
View on Chainz β†—

Height

#2,119,851

Difficulty

10.911615

Transactions

1

Size

201 B

Version

2

Bits

0ae95f9d

Nonce

168,725,882

Timestamp

5/16/2017, 11:50:04 PM

Confirmations

4,712,831

Mined by

⛏️ P2SHAatZWXxekxivonFfdhQCi5zkg6sD7VJVem

Merkle Root

5f3731479e387343eb18d1c8695eab769fe4487d3a415d5ec65bcfb47867218d
Transactions (1)
Coinbase5f3731479e3873…5bcfb47867218d
1 in β†’ 1 out8.3900 XPM110 B
AatZWXxe…sD7VJVem
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.

8.019 Γ— 10⁹⁢(97-digit number)
80199995393856533038…37103623798819860479
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
8.019 Γ— 10⁹⁢(97-digit number)
80199995393856533038…37103623798819860479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.019 Γ— 10⁹⁢(97-digit number)
80199995393856533038…37103623798819860481
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
1.603 Γ— 10⁹⁷(98-digit number)
16039999078771306607…74207247597639720959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.603 Γ— 10⁹⁷(98-digit number)
16039999078771306607…74207247597639720961
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
3.207 Γ— 10⁹⁷(98-digit number)
32079998157542613215…48414495195279441919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.207 Γ— 10⁹⁷(98-digit number)
32079998157542613215…48414495195279441921
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
6.415 Γ— 10⁹⁷(98-digit number)
64159996315085226430…96828990390558883839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.415 Γ— 10⁹⁷(98-digit number)
64159996315085226430…96828990390558883841
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
1.283 Γ— 10⁹⁸(99-digit number)
12831999263017045286…93657980781117767679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.283 Γ— 10⁹⁸(99-digit number)
12831999263017045286…93657980781117767681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,905,610 XPMΒ·at block #6,832,681 Β· updates every 60s
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