XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,612,690

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2016, 6:21:24 PM Β· Difficulty 10.6013 Β· 5,230,179 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fd7646125d7fb656c130b0a77811d2995a29bd9242647b6797989cbbea9a5807
View on Chainz β†—

Height

#1,612,690

Difficulty

10.601322

Transactions

1

Size

199 B

Version

2

Bits

0a99f03b

Nonce

1,682,946,652

Timestamp

6/3/2016, 6:21:24 PM

Confirmations

5,230,179

Mined by

⛏️ P2SHAVnrGqLNEuk3LFAyZbVvpgNoXWF1EVuryL

Merkle Root

970249c45d9009bc54aacb0284f77ad5b22d2417e7029c2a71af2e9fc0ebb815
Transactions (1)
Coinbase970249c45d9009…af2e9fc0ebb815
1 in β†’ 1 out8.8800 XPM109 B
AVnrGqLN…F1EVuryL
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.

1.394 Γ— 10⁹⁴(95-digit number)
13942585668028906821…35175637063282769759
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
1.394 Γ— 10⁹⁴(95-digit number)
13942585668028906821…35175637063282769759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.394 Γ— 10⁹⁴(95-digit number)
13942585668028906821…35175637063282769761
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
2.788 Γ— 10⁹⁴(95-digit number)
27885171336057813643…70351274126565539519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.788 Γ— 10⁹⁴(95-digit number)
27885171336057813643…70351274126565539521
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
5.577 Γ— 10⁹⁴(95-digit number)
55770342672115627286…40702548253131079039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.577 Γ— 10⁹⁴(95-digit number)
55770342672115627286…40702548253131079041
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
1.115 Γ— 10⁹⁡(96-digit number)
11154068534423125457…81405096506262158079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.115 Γ— 10⁹⁡(96-digit number)
11154068534423125457…81405096506262158081
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
2.230 Γ— 10⁹⁡(96-digit number)
22308137068846250914…62810193012524316159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.230 Γ— 10⁹⁡(96-digit number)
22308137068846250914…62810193012524316161
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:57,987,295 XPMΒ·at block #6,842,868 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy