XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,154,003

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/24/2019, 11:08:48 PM Β· Difficulty 11.3160 Β· 3,683,459 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c9ad096fcd7393c9f146026f323af872ccadbc211fd6e7b1c65c41dbd4cbe7e0
View on Chainz β†—

Height

#3,154,003

Difficulty

11.316006

Transactions

2

Size

391 B

Version

2

Bits

0b50e5cc

Nonce

749,014,047

Timestamp

4/24/2019, 11:08:48 PM

Confirmations

3,683,459

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

0137d6c2a2e8a1c256e0a694d716c620126c9007fc3216231b7bd4f2db88b4e0
Transactions (2)
Coinbaseb4d3484e4b73a6…ef1efe06e44684
1 in β†’ 1 out7.8100 XPM110 B
ARbm48qR…9xQc8DBX
cf711f00f0cd36…c51cfccaaddd82
1 in β†’ 1 out623.7300 XPM191 B
AeTHTL7A…vT1872bk
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.

3.062 Γ— 10⁹³(94-digit number)
30627800938689643587…99023593030495288319
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
3.062 Γ— 10⁹³(94-digit number)
30627800938689643587…99023593030495288319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.062 Γ— 10⁹³(94-digit number)
30627800938689643587…99023593030495288321
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
6.125 Γ— 10⁹³(94-digit number)
61255601877379287175…98047186060990576639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.125 Γ— 10⁹³(94-digit number)
61255601877379287175…98047186060990576641
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
1.225 Γ— 10⁹⁴(95-digit number)
12251120375475857435…96094372121981153279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.225 Γ— 10⁹⁴(95-digit number)
12251120375475857435…96094372121981153281
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
2.450 Γ— 10⁹⁴(95-digit number)
24502240750951714870…92188744243962306559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.450 Γ— 10⁹⁴(95-digit number)
24502240750951714870…92188744243962306561
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
4.900 Γ— 10⁹⁴(95-digit number)
49004481501903429740…84377488487924613119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.900 Γ— 10⁹⁴(95-digit number)
49004481501903429740…84377488487924613121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.800 Γ— 10⁹⁴(95-digit number)
98008963003806859480…68754976975849226239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,944,015 XPMΒ·at block #6,837,461 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