XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,601,726

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/5/2018, 8:05:42 PM Β· Difficulty 11.3156 Β· 4,238,056 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
69fae37123152b7364b0e9b907faa65e85c007d47a5f292d933815b201e628f1
View on Chainz β†—

Height

#2,601,726

Difficulty

11.315569

Transactions

1

Size

199 B

Version

2

Bits

0b50c927

Nonce

217,406,342

Timestamp

4/5/2018, 8:05:42 PM

Confirmations

4,238,056

Mined by

⛏️ P2SHAZQ1fxs77vwkVaSia9GHc3gQsbwQv3JdiP

Merkle Root

e75334d1cb4b35b8370bce715d12bca8c51673862f32f9ab78e64a60c10e7f57
Transactions (1)
Coinbasee75334d1cb4b35…e64a60c10e7f57
1 in β†’ 1 out7.8000 XPM109 B
AZQ1fxs7…wQv3JdiP
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.

3.865 Γ— 10⁹⁴(95-digit number)
38652904772163624396…02083496737460329169
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
3.865 Γ— 10⁹⁴(95-digit number)
38652904772163624396…02083496737460329169
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.865 Γ— 10⁹⁴(95-digit number)
38652904772163624396…02083496737460329171
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
7.730 Γ— 10⁹⁴(95-digit number)
77305809544327248792…04166993474920658339
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.730 Γ— 10⁹⁴(95-digit number)
77305809544327248792…04166993474920658341
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
1.546 Γ— 10⁹⁡(96-digit number)
15461161908865449758…08333986949841316679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.546 Γ— 10⁹⁡(96-digit number)
15461161908865449758…08333986949841316681
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
3.092 Γ— 10⁹⁡(96-digit number)
30922323817730899516…16667973899682633359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.092 Γ— 10⁹⁡(96-digit number)
30922323817730899516…16667973899682633361
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
6.184 Γ— 10⁹⁡(96-digit number)
61844647635461799033…33335947799365266719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.184 Γ— 10⁹⁡(96-digit number)
61844647635461799033…33335947799365266721
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
1.236 Γ— 10⁹⁢(97-digit number)
12368929527092359806…66671895598730533439
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:57,962,546 XPMΒ·at block #6,839,781 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