XPM Prime Explorer symbol
XPMPrime Explorer

Block #182,590

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/27/2013, 10:37:01 AM Β· Difficulty 9.8575 Β· 6,623,106 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4bc74ebdbbc7f9cd34b6f256284880fd48f3450a7ca35ba04ef03e74b4950225
View on Chainz β†—

Height

#182,590

Difficulty

9.857484

Transactions

1

Size

199 B

Version

2

Bits

09db841a

Nonce

95,935

Timestamp

9/27/2013, 10:37:01 AM

Confirmations

6,623,106

Mined by

⛏️ P2SHAUm1UXE6PTt11eQB2DXhcmZJbwSTx2UrXW

Merkle Root

4f82fa5e88509e34e0b256f199a211a4509ea275ac2e02e4f637de0911242f58
Transactions (1)
Coinbase4f82fa5e88509e…37de0911242f58
1 in β†’ 1 out10.2800 XPM109 B
AUm1UXE6…STx2UrXW
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.

2.959 Γ— 10⁹⁴(95-digit number)
29590011217344665337…13673177716469419839
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
2.959 Γ— 10⁹⁴(95-digit number)
29590011217344665337…13673177716469419839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.959 Γ— 10⁹⁴(95-digit number)
29590011217344665337…13673177716469419841
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
5.918 Γ— 10⁹⁴(95-digit number)
59180022434689330675…27346355432938839679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.918 Γ— 10⁹⁴(95-digit number)
59180022434689330675…27346355432938839681
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
1.183 Γ— 10⁹⁡(96-digit number)
11836004486937866135…54692710865877679359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.183 Γ— 10⁹⁡(96-digit number)
11836004486937866135…54692710865877679361
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
2.367 Γ— 10⁹⁡(96-digit number)
23672008973875732270…09385421731755358719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.367 Γ— 10⁹⁡(96-digit number)
23672008973875732270…09385421731755358721
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
4.734 Γ— 10⁹⁡(96-digit number)
47344017947751464540…18770843463510717439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,689,649 XPMΒ·at block #6,805,695 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