XPM Prime Explorer symbol
XPMPrime Explorer

Block #387,921

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/3/2014, 11:12:14 AM Β· Difficulty 10.4155 Β· 6,420,255 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
96d10f6c8c9d2bb57f30b67b54ec33096dc4fedc2c37d43ea3de9beb840d1d01
View on Chainz β†—

Height

#387,921

Difficulty

10.415457

Transactions

1

Size

202 B

Version

2

Bits

0a6a5b61

Nonce

72,986

Timestamp

2/3/2014, 11:12:14 AM

Confirmations

6,420,255

Mined by

⛏️ P2SHAJitpuBFBWRraKw6JNZ4K3FnMosUNZF3e4

Merkle Root

3fdd6b905df8944e1c394ec4647598b28fc2c39f8a55f97b7debd9e16b23998a
Transactions (1)
Coinbase3fdd6b905df894…ebd9e16b23998a
1 in β†’ 1 out9.2000 XPM111 B
AJitpuBF…sUNZF3e4
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.

2.125 Γ— 10⁹⁢(97-digit number)
21250012722588089806…92299545141534657919
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
2.125 Γ— 10⁹⁢(97-digit number)
21250012722588089806…92299545141534657919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.125 Γ— 10⁹⁢(97-digit number)
21250012722588089806…92299545141534657921
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
4.250 Γ— 10⁹⁢(97-digit number)
42500025445176179613…84599090283069315839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.250 Γ— 10⁹⁢(97-digit number)
42500025445176179613…84599090283069315841
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
8.500 Γ— 10⁹⁢(97-digit number)
85000050890352359227…69198180566138631679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.500 Γ— 10⁹⁢(97-digit number)
85000050890352359227…69198180566138631681
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
1.700 Γ— 10⁹⁷(98-digit number)
17000010178070471845…38396361132277263359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.700 Γ— 10⁹⁷(98-digit number)
17000010178070471845…38396361132277263361
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
3.400 Γ— 10⁹⁷(98-digit number)
34000020356140943691…76792722264554526719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.400 Γ— 10⁹⁷(98-digit number)
34000020356140943691…76792722264554526721
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:57,709,456 XPMΒ·at block #6,808,175 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