XPM Prime Explorer symbol
XPMPrime Explorer

Block #387,015

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/2/2014, 8:17:28 PM Β· Difficulty 10.4137 Β· 6,422,282 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4e545a090cc08ffe674e96998f494956a403bd445550efaab30ff8c16760348f
View on Chainz β†—

Height

#387,015

Difficulty

10.413735

Transactions

2

Size

392 B

Version

2

Bits

0a69ea91

Nonce

225,154

Timestamp

2/2/2014, 8:17:28 PM

Confirmations

6,422,282

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4d20117cd3539071d1a89f2437bfa35a73b980572ae50970f4fb3df7dbc3822f
Transactions (2)
Coinbase9e82d84c0d0c9c…a6afc4d2745015
1 in β†’ 1 out9.2200 XPM110 B
AeKNrjNj…1NEq95Ta
63f770e27a32bf…4b9a6d1df792fd
1 in β†’ 1 out2.9915 XPM191 B
AWqeLAbV…fpe1Fr2i
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.

1.118 Γ— 10⁹⁷(98-digit number)
11182198555179253271…78901831056950231039
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
1.118 Γ— 10⁹⁷(98-digit number)
11182198555179253271…78901831056950231039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.118 Γ— 10⁹⁷(98-digit number)
11182198555179253271…78901831056950231041
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
2.236 Γ— 10⁹⁷(98-digit number)
22364397110358506543…57803662113900462079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.236 Γ— 10⁹⁷(98-digit number)
22364397110358506543…57803662113900462081
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
4.472 Γ— 10⁹⁷(98-digit number)
44728794220717013086…15607324227800924159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.472 Γ— 10⁹⁷(98-digit number)
44728794220717013086…15607324227800924161
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
8.945 Γ— 10⁹⁷(98-digit number)
89457588441434026172…31214648455601848319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.945 Γ— 10⁹⁷(98-digit number)
89457588441434026172…31214648455601848321
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
1.789 Γ— 10⁹⁸(99-digit number)
17891517688286805234…62429296911203696639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.789 Γ— 10⁹⁸(99-digit number)
17891517688286805234…62429296911203696641
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:57,718,446 XPMΒ·at block #6,809,296 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