XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,700,493

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/11/2018, 5:30:42 AM Β· Difficulty 11.6377 Β· 4,144,855 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6f7b9095d2645ea96665c5e8246ad7129fd13c0d43d351d54040939e0ce01943
View on Chainz β†—

Height

#2,700,493

Difficulty

11.637715

Transactions

2

Size

392 B

Version

2

Bits

0ba3414b

Nonce

444,502,259

Timestamp

6/11/2018, 5:30:42 AM

Confirmations

4,144,855

Mined by

⛏️ P2SHAb7jC92SxfWWPwySXfGZyDWYGHa1HhJooS

Merkle Root

3c0deb54069877c90a8128b4503154c8d74c3ece61bd6f357181c81bb70e4672
Transactions (2)
Coinbase2afe9c27ee1217…60abcff150d40a
1 in β†’ 1 out7.3800 XPM110 B
Ab7jC92S…a1HhJooS
5c5c1638418b78…1a423db0f8e7d8
1 in β†’ 1 out3.9900 XPM192 B
AW1VQNrh…AuseDjPW
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.

4.457 Γ— 10⁹⁡(96-digit number)
44575124445402786981…43201571665870666879
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
4.457 Γ— 10⁹⁡(96-digit number)
44575124445402786981…43201571665870666879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.457 Γ— 10⁹⁡(96-digit number)
44575124445402786981…43201571665870666881
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
8.915 Γ— 10⁹⁡(96-digit number)
89150248890805573963…86403143331741333759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.915 Γ— 10⁹⁡(96-digit number)
89150248890805573963…86403143331741333761
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
1.783 Γ— 10⁹⁢(97-digit number)
17830049778161114792…72806286663482667519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.783 Γ— 10⁹⁢(97-digit number)
17830049778161114792…72806286663482667521
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
3.566 Γ— 10⁹⁢(97-digit number)
35660099556322229585…45612573326965335039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.566 Γ— 10⁹⁢(97-digit number)
35660099556322229585…45612573326965335041
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
7.132 Γ— 10⁹⁢(97-digit number)
71320199112644459170…91225146653930670079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.132 Γ— 10⁹⁢(97-digit number)
71320199112644459170…91225146653930670081
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
1.426 Γ— 10⁹⁷(98-digit number)
14264039822528891834…82450293307861340159
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:58,007,226 XPMΒ·at block #6,845,347 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