XPM Prime Explorer symbol
XPMPrime Explorer

Block #35,583

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 8:17:17 AM Β· Difficulty 7.9946 Β· 6,772,258 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
41d3d67624a8975a5944cf6c13e987cc559d8162384eb7eab644812e93c218b6
View on Chainz β†—

Height

#35,583

Difficulty

7.994566

Transactions

1

Size

201 B

Version

2

Bits

07fe9be1

Nonce

73

Timestamp

7/14/2013, 8:17:17 AM

Confirmations

6,772,258

Mined by

⛏️ P2SHAV6P7enUMtWL6sjxBf1aCsLJbsVLHeixvR

Merkle Root

e6547021ff415466af64cf63b976b2b279ef18e79a4c361755218fc140e9206d
Transactions (1)
Coinbasee6547021ff4154…218fc140e9206d
1 in β†’ 1 out15.6300 XPM109 B
AV6P7enU…VLHeixvR
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.

7.199 Γ— 10⁹⁹(100-digit number)
71998127028270634828…90470828222217995109
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
7.199 Γ— 10⁹⁹(100-digit number)
71998127028270634828…90470828222217995109
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.199 Γ— 10⁹⁹(100-digit number)
71998127028270634828…90470828222217995111
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
1.439 Γ— 10¹⁰⁰(101-digit number)
14399625405654126965…80941656444435990219
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.439 Γ— 10¹⁰⁰(101-digit number)
14399625405654126965…80941656444435990221
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
2.879 Γ— 10¹⁰⁰(101-digit number)
28799250811308253931…61883312888871980439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.879 Γ— 10¹⁰⁰(101-digit number)
28799250811308253931…61883312888871980441
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
5.759 Γ— 10¹⁰⁰(101-digit number)
57598501622616507862…23766625777743960879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.759 Γ— 10¹⁰⁰(101-digit number)
57598501622616507862…23766625777743960881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,706,766 XPMΒ·at block #6,807,840 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