XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,312,173

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/4/2015, 10:22:15 AM Β· Difficulty 10.8523 Β· 5,495,956 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a9795d83dcf8e295735a92cb974d93380ab7c733ef3f30af9e995b354542e0e8
View on Chainz β†—

Height

#1,312,173

Difficulty

10.852286

Transactions

2

Size

16.28 KB

Version

2

Bits

0ada2f68

Nonce

364,897,195

Timestamp

11/4/2015, 10:22:15 AM

Confirmations

5,495,956

Mined by

⛏️ P2SHASszaALAsM9Ev1rPNe4fiMDozYbL8ahpfU

Merkle Root

c46ee13725a551b651d0c2235f6e37b6a34ab0796ced23cf9dc39095a5b49de2
Transactions (2)
Coinbase5de41a987c6a8e…1ddcbe9e3fb00b
1 in β†’ 1 out8.6700 XPM110 B
ASszaALA…bL8ahpfU
ec6fd398e62518…cd00110767f8ff
111 in β†’ 1 out233.5237 XPM16.09 KB
AeNYqawm…GzYnccKL
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.

2.086 Γ— 10⁹⁴(95-digit number)
20861447968947702947…25286335950019325599
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
2.086 Γ— 10⁹⁴(95-digit number)
20861447968947702947…25286335950019325599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.086 Γ— 10⁹⁴(95-digit number)
20861447968947702947…25286335950019325601
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
4.172 Γ— 10⁹⁴(95-digit number)
41722895937895405895…50572671900038651199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.172 Γ— 10⁹⁴(95-digit number)
41722895937895405895…50572671900038651201
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
8.344 Γ— 10⁹⁴(95-digit number)
83445791875790811790…01145343800077302399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.344 Γ— 10⁹⁴(95-digit number)
83445791875790811790…01145343800077302401
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
1.668 Γ— 10⁹⁡(96-digit number)
16689158375158162358…02290687600154604799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.668 Γ— 10⁹⁡(96-digit number)
16689158375158162358…02290687600154604801
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
3.337 Γ— 10⁹⁡(96-digit number)
33378316750316324716…04581375200309209599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.337 Γ— 10⁹⁡(96-digit number)
33378316750316324716…04581375200309209601
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:57,709,073 XPMΒ·at block #6,808,128 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