XPM Prime Explorer symbol
XPMPrime Explorer

Block #318,223

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/18/2013, 5:24:23 AM Β· Difficulty 10.1590 Β· 6,476,544 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f47ee927b3a309e8cf60f515d2aa253d0c830546507ebd8733a62ceee1569116
View on Chainz β†—

Height

#318,223

Difficulty

10.158958

Transactions

1

Size

205 B

Version

2

Bits

0a28b180

Nonce

44,360

Timestamp

12/18/2013, 5:24:23 AM

Confirmations

6,476,544

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

d9090cfd5e8af92dd4df516440fd693f99ed66e701a3af2f1dc31cbdbc4eed64
Transactions (1)
Coinbased9090cfd5e8af9…c31cbdbc4eed64
1 in β†’ 1 out9.6700 XPM116 B
AbwWkWZt…kawDhufa
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.

1.036 Γ— 10⁹³(94-digit number)
10367902943779922683…93430322028692602039
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
1.036 Γ— 10⁹³(94-digit number)
10367902943779922683…93430322028692602039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.036 Γ— 10⁹³(94-digit number)
10367902943779922683…93430322028692602041
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
2.073 Γ— 10⁹³(94-digit number)
20735805887559845367…86860644057385204079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.073 Γ— 10⁹³(94-digit number)
20735805887559845367…86860644057385204081
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
4.147 Γ— 10⁹³(94-digit number)
41471611775119690734…73721288114770408159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.147 Γ— 10⁹³(94-digit number)
41471611775119690734…73721288114770408161
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
8.294 Γ— 10⁹³(94-digit number)
82943223550239381469…47442576229540816319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.294 Γ— 10⁹³(94-digit number)
82943223550239381469…47442576229540816321
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
1.658 Γ— 10⁹⁴(95-digit number)
16588644710047876293…94885152459081632639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.658 Γ— 10⁹⁴(95-digit number)
16588644710047876293…94885152459081632641
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:57,602,185 XPMΒ·at block #6,794,766 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