XPM Prime Explorer symbol
XPMPrime Explorer

Block #317,749

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/17/2013, 9:54:43 PM Β· Difficulty 10.1548 Β· 6,491,054 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5672309f489d7bd1bbf4bc052d860b72593655dcded5e3df9e843eaaa58ef998
View on Chainz β†—

Height

#317,749

Difficulty

10.154841

Transactions

1

Size

202 B

Version

2

Bits

0a27a3b0

Nonce

253,638

Timestamp

12/17/2013, 9:54:43 PM

Confirmations

6,491,054

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e301234d6d9e876e7760258555d12da1b61f026e698d36301f56d6ccd2350722
Transactions (1)
Coinbasee301234d6d9e87…56d6ccd2350722
1 in β†’ 1 out9.6800 XPM110 B
AeKNrjNj…1NEq95Ta
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.

4.090 Γ— 10⁹⁹(100-digit number)
40900119562411455232…09127862876753167999
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
4.090 Γ— 10⁹⁹(100-digit number)
40900119562411455232…09127862876753167999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.090 Γ— 10⁹⁹(100-digit number)
40900119562411455232…09127862876753168001
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
8.180 Γ— 10⁹⁹(100-digit number)
81800239124822910464…18255725753506335999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.180 Γ— 10⁹⁹(100-digit number)
81800239124822910464…18255725753506336001
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
1.636 Γ— 10¹⁰⁰(101-digit number)
16360047824964582092…36511451507012671999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.636 Γ— 10¹⁰⁰(101-digit number)
16360047824964582092…36511451507012672001
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
3.272 Γ— 10¹⁰⁰(101-digit number)
32720095649929164185…73022903014025343999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.272 Γ— 10¹⁰⁰(101-digit number)
32720095649929164185…73022903014025344001
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
6.544 Γ— 10¹⁰⁰(101-digit number)
65440191299858328371…46045806028050687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.544 Γ— 10¹⁰⁰(101-digit number)
65440191299858328371…46045806028050688001
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:57,714,478 XPMΒ·at block #6,808,802 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