XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,843,061

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2018, 7:45:08 AM Β· Difficulty 11.7249 Β· 3,990,942 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
754063fcd3cc373684d639bb9b8608e133fe82fabbcb8e41deac66b137cd4dc5
View on Chainz β†—

Height

#2,843,061

Difficulty

11.724872

Transactions

1

Size

199 B

Version

2

Bits

0bb9913d

Nonce

63,991,021

Timestamp

9/17/2018, 7:45:08 AM

Confirmations

3,990,942

Mined by

⛏️ P2SHAcEiB4FMVEcvFeR6QA51UJ2ViVMFyvtFc5

Merkle Root

e075e2ce8891490d5854dc5172d63984bfad04fd3365f8f5f845c32ebc14a2fc
Transactions (1)
Coinbasee075e2ce889149…45c32ebc14a2fc
1 in β†’ 1 out7.2600 XPM110 B
AcEiB4FM…MFyvtFc5
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.

8.487 Γ— 10⁹²(93-digit number)
84876641043276986491…33072654465342994199
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
8.487 Γ— 10⁹²(93-digit number)
84876641043276986491…33072654465342994199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.487 Γ— 10⁹²(93-digit number)
84876641043276986491…33072654465342994201
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
1.697 Γ— 10⁹³(94-digit number)
16975328208655397298…66145308930685988399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.697 Γ— 10⁹³(94-digit number)
16975328208655397298…66145308930685988401
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
3.395 Γ— 10⁹³(94-digit number)
33950656417310794596…32290617861371976799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.395 Γ— 10⁹³(94-digit number)
33950656417310794596…32290617861371976801
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
6.790 Γ— 10⁹³(94-digit number)
67901312834621589193…64581235722743953599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.790 Γ— 10⁹³(94-digit number)
67901312834621589193…64581235722743953601
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
1.358 Γ— 10⁹⁴(95-digit number)
13580262566924317838…29162471445487907199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.358 Γ— 10⁹⁴(95-digit number)
13580262566924317838…29162471445487907201
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
2.716 Γ— 10⁹⁴(95-digit number)
27160525133848635677…58324942890975814399
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:57,916,251 XPMΒ·at block #6,834,002 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