XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,524,591

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/3/2016, 1:11:39 PM Β· Difficulty 10.6009 Β· 5,293,261 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c9c5e4ceb485419f0100f0fc9228507ed07440c04bbefa362362376bb1b1d0ea
View on Chainz β†—

Height

#1,524,591

Difficulty

10.600933

Transactions

2

Size

21.93 KB

Version

2

Bits

0a99d6c7

Nonce

790,480,187

Timestamp

4/3/2016, 1:11:39 PM

Confirmations

5,293,261

Mined by

⛏️ P2SHANDzS2UEVSFC4uPney5BwghJEK1WnXrcpZ

Merkle Root

78b3542040b2b6523d9b2c5618e3b198524ece9b4c85f58d833418422377ef05
Transactions (2)
Coinbase545fb1d92c012b…2386ea6352bbc6
1 in β†’ 1 out9.1100 XPM110 B
ANDzS2UE…1WnXrcpZ
bb9bea85d506d1…42fdbffb9ecadf
150 in β†’ 1 out2.0000 XPM21.73 KB
AW9z6iyE…ZMok5rfx
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.

1.949 Γ— 10⁹⁡(96-digit number)
19495151732088199953…50846026382762643199
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
1.949 Γ— 10⁹⁡(96-digit number)
19495151732088199953…50846026382762643199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.949 Γ— 10⁹⁡(96-digit number)
19495151732088199953…50846026382762643201
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
3.899 Γ— 10⁹⁡(96-digit number)
38990303464176399907…01692052765525286399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.899 Γ— 10⁹⁡(96-digit number)
38990303464176399907…01692052765525286401
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
7.798 Γ— 10⁹⁡(96-digit number)
77980606928352799814…03384105531050572799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.798 Γ— 10⁹⁡(96-digit number)
77980606928352799814…03384105531050572801
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
1.559 Γ— 10⁹⁢(97-digit number)
15596121385670559962…06768211062101145599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.559 Γ— 10⁹⁢(97-digit number)
15596121385670559962…06768211062101145601
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
3.119 Γ— 10⁹⁢(97-digit number)
31192242771341119925…13536422124202291199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.119 Γ— 10⁹⁢(97-digit number)
31192242771341119925…13536422124202291201
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:57,786,882 XPMΒ·at block #6,817,851 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.
Privacy PolicyΒ·
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