XPM Prime Explorer symbol
XPMPrime Explorer

Block #354,575

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2014, 3:15:10 PM Β· Difficulty 10.3459 Β· 6,487,133 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b2af06c84cde04ced8102b1bf0c4028c74418fcce3bed542566e683529a7743c
View on Chainz β†—

Height

#354,575

Difficulty

10.345898

Transactions

2

Size

1.14 KB

Version

2

Bits

0a588cc6

Nonce

105,935

Timestamp

1/11/2014, 3:15:10 PM

Confirmations

6,487,133

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5ebbdd81ae5650c953131424bbf3d8a4e85e8467944008aa165221b145630f9e
Transactions (2)
Coinbase381d831db69cd0…d04c67a4e57455
1 in β†’ 1 out9.3400 XPM110 B
AeKNrjNj…1NEq95Ta
426fa7214d2e03…0d29133513e11a
6 in β†’ 2 out3.0882 XPM964 B
AdP5mdo4…i8cZ6v3zAPz2aPdD…ADp7YvB3
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.

1.652 Γ— 10⁹⁸(99-digit number)
16523945330525841176…82368761590998058879
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
1.652 Γ— 10⁹⁸(99-digit number)
16523945330525841176…82368761590998058879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.652 Γ— 10⁹⁸(99-digit number)
16523945330525841176…82368761590998058881
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
3.304 Γ— 10⁹⁸(99-digit number)
33047890661051682352…64737523181996117759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.304 Γ— 10⁹⁸(99-digit number)
33047890661051682352…64737523181996117761
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
6.609 Γ— 10⁹⁸(99-digit number)
66095781322103364705…29475046363992235519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.609 Γ— 10⁹⁸(99-digit number)
66095781322103364705…29475046363992235521
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
1.321 Γ— 10⁹⁹(100-digit number)
13219156264420672941…58950092727984471039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.321 Γ— 10⁹⁹(100-digit number)
13219156264420672941…58950092727984471041
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
2.643 Γ— 10⁹⁹(100-digit number)
26438312528841345882…17900185455968942079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.643 Γ— 10⁹⁹(100-digit number)
26438312528841345882…17900185455968942081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,978,042 XPMΒ·at block #6,841,707 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