XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,716,866

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/14/2016, 1:21:13 PM Β· Difficulty 10.6640 Β· 5,091,194 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
567a595edc9b218e3e7a01d74a1ede28fc1420ee6d139b03921add618ef29c16
View on Chainz β†—

Height

#1,716,866

Difficulty

10.664009

Transactions

1

Size

242 B

Version

2

Bits

0aa9fc7f

Nonce

71,402,476

Timestamp

8/14/2016, 1:21:13 PM

Confirmations

5,091,194

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

ce58bdb7aaaf680eac7c7bda2ae28c81029a05e5b8bc0368a8418c3567f9295b
Transactions (1)
Coinbasece58bdb7aaaf68…418c3567f9295b
1 in β†’ 2 out8.7800 XPM152 B
AKjaKd2K…DPsqUE8eAXbk7f7A…Tx7JECPG
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.

3.434 Γ— 10⁹⁡(96-digit number)
34348914908645357768…56653613131625154879
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
3.434 Γ— 10⁹⁡(96-digit number)
34348914908645357768…56653613131625154879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.434 Γ— 10⁹⁡(96-digit number)
34348914908645357768…56653613131625154881
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
6.869 Γ— 10⁹⁡(96-digit number)
68697829817290715537…13307226263250309759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.869 Γ— 10⁹⁡(96-digit number)
68697829817290715537…13307226263250309761
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
1.373 Γ— 10⁹⁢(97-digit number)
13739565963458143107…26614452526500619519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.373 Γ— 10⁹⁢(97-digit number)
13739565963458143107…26614452526500619521
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
2.747 Γ— 10⁹⁢(97-digit number)
27479131926916286214…53228905053001239039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.747 Γ— 10⁹⁢(97-digit number)
27479131926916286214…53228905053001239041
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
5.495 Γ— 10⁹⁢(97-digit number)
54958263853832572429…06457810106002478079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.495 Γ— 10⁹⁢(97-digit number)
54958263853832572429…06457810106002478081
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:57,708,524 XPMΒ·at block #6,808,059 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.
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