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Block #2,098,489

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2017, 3:39:03 PM Β· Difficulty 10.8637 Β· 4,743,917 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2b87462a4771f28ed69f22455f0c1dfdf2bd2d6f7dcf718e3f8ddb5b9f8a8066
View on Chainz β†—

Height

#2,098,489

Difficulty

10.863744

Transactions

1

Size

199 B

Version

2

Bits

0add1e54

Nonce

260,698,608

Timestamp

5/3/2017, 3:39:03 PM

Confirmations

4,743,917

Mined by

⛏️ P2SHAZYqquZ3s2NttF5LswcY5jDzbPFduKEjwn

Merkle Root

6aa2c05dc8582ff8340604536f23227b648e5b9744bb59d73905966ffa51cbad
Transactions (1)
Coinbase6aa2c05dc8582f…05966ffa51cbad
1 in β†’ 1 out8.4600 XPM109 B
AZYqquZ3…FduKEjwn
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.

5.832 Γ— 10⁹⁴(95-digit number)
58324234547164628776…17931219904932653279
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
5.832 Γ— 10⁹⁴(95-digit number)
58324234547164628776…17931219904932653279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.832 Γ— 10⁹⁴(95-digit number)
58324234547164628776…17931219904932653281
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
1.166 Γ— 10⁹⁡(96-digit number)
11664846909432925755…35862439809865306559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.166 Γ— 10⁹⁡(96-digit number)
11664846909432925755…35862439809865306561
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
2.332 Γ— 10⁹⁡(96-digit number)
23329693818865851510…71724879619730613119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.332 Γ— 10⁹⁡(96-digit number)
23329693818865851510…71724879619730613121
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
4.665 Γ— 10⁹⁡(96-digit number)
46659387637731703021…43449759239461226239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.665 Γ— 10⁹⁡(96-digit number)
46659387637731703021…43449759239461226241
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
9.331 Γ— 10⁹⁡(96-digit number)
93318775275463406042…86899518478922452479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.331 Γ— 10⁹⁡(96-digit number)
93318775275463406042…86899518478922452481
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:57,983,660 XPMΒ·at block #6,842,405 Β· updates every 60s
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