XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,130,714

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2017, 2:48:05 PM Β· Difficulty 10.9100 Β· 4,714,585 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f5dffd55c1f963c390766975395d2dce95b2dce167cfbbc60756b0ac30916a85
View on Chainz β†—

Height

#2,130,714

Difficulty

10.909955

Transactions

2

Size

1017 B

Version

2

Bits

0ae8f2ce

Nonce

549,527,518

Timestamp

5/24/2017, 2:48:05 PM

Confirmations

4,714,585

Mined by

⛏️ P2SHAXC4PUPth4QNvUayhRYUUPdHRTrvjTkqHG

Merkle Root

a373ede03351a7e2bdf5c0b10b39917da01f5f69c31c44dfb90bbc91c3e94ec5
Transactions (2)
Coinbasedaa06dc0b7393e…7580fcebf02c0d
1 in β†’ 1 out8.4000 XPM110 B
AXC4PUPt…rvjTkqHG
82d2d3d6bd766d…36ff928209b1fd
5 in β†’ 2 out2000.0179 XPM817 B
AdB69zJh…s7M6DLc5ARaNCeSx…b8M3uhxY
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.

1.070 Γ— 10⁹⁡(96-digit number)
10704961900252699950…60347577831869266559
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
1.070 Γ— 10⁹⁡(96-digit number)
10704961900252699950…60347577831869266559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.070 Γ— 10⁹⁡(96-digit number)
10704961900252699950…60347577831869266561
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
2.140 Γ— 10⁹⁡(96-digit number)
21409923800505399900…20695155663738533119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.140 Γ— 10⁹⁡(96-digit number)
21409923800505399900…20695155663738533121
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
4.281 Γ— 10⁹⁡(96-digit number)
42819847601010799801…41390311327477066239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.281 Γ— 10⁹⁡(96-digit number)
42819847601010799801…41390311327477066241
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
8.563 Γ— 10⁹⁡(96-digit number)
85639695202021599603…82780622654954132479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.563 Γ— 10⁹⁡(96-digit number)
85639695202021599603…82780622654954132481
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
1.712 Γ— 10⁹⁢(97-digit number)
17127939040404319920…65561245309908264959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.712 Γ— 10⁹⁢(97-digit number)
17127939040404319920…65561245309908264961
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
3.425 Γ— 10⁹⁢(97-digit number)
34255878080808639841…31122490619816529919
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:58,006,831 XPMΒ·at block #6,845,298 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