XPM Prime Explorer symbol
XPMPrime Explorer

Block #413,257

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/21/2014, 2:56:28 AM Β· Difficulty 10.4150 Β· 6,395,939 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
44f5cfde9eb5e42dc4df1578af98bc39f2ddb2ac148598474238f12ade900aa0
View on Chainz β†—

Height

#413,257

Difficulty

10.415020

Transactions

2

Size

1.16 KB

Version

2

Bits

0a6a3ebf

Nonce

160,377

Timestamp

2/21/2014, 2:56:28 AM

Confirmations

6,395,939

Mined by

⛏️ INAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

2d710657732b71adfc160fef7735aad953a8ad7dd44761b86f02ca996b2f2bc1
Transactions (2)
Coinbaseeefdbc4ddbfb80…c83b8cc75c2571
1 in β†’ 2 out9.2100 XPM131 B
AMVf7Jrg…xd5AVR7CAJno7LX2…vo4wdWtY
2ac3d1a9cf7e25…39a051687fa841
6 in β†’ 2 out50.0193 XPM967 B
ALfKeL39…UDyJy1kHAH67zFsv…5hypXjUt
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.

3.923 Γ— 10⁹⁷(98-digit number)
39231727481693646614…07894759132452262399
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
3.923 Γ— 10⁹⁷(98-digit number)
39231727481693646614…07894759132452262399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.923 Γ— 10⁹⁷(98-digit number)
39231727481693646614…07894759132452262401
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
7.846 Γ— 10⁹⁷(98-digit number)
78463454963387293228…15789518264904524799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.846 Γ— 10⁹⁷(98-digit number)
78463454963387293228…15789518264904524801
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
1.569 Γ— 10⁹⁸(99-digit number)
15692690992677458645…31579036529809049599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.569 Γ— 10⁹⁸(99-digit number)
15692690992677458645…31579036529809049601
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
3.138 Γ— 10⁹⁸(99-digit number)
31385381985354917291…63158073059618099199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.138 Γ— 10⁹⁸(99-digit number)
31385381985354917291…63158073059618099201
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
6.277 Γ— 10⁹⁸(99-digit number)
62770763970709834582…26316146119236198399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.277 Γ— 10⁹⁸(99-digit number)
62770763970709834582…26316146119236198401
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:57,717,626 XPMΒ·at block #6,809,195 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