XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,059,252

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/6/2017, 7:30:15 PM Β· Difficulty 10.8455 Β· 4,768,106 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4f1c72f991c6bc1b44cee2a23b4d14e3d89d028e64fc0af91f1c6fd88c16c9ed
View on Chainz β†—

Height

#2,059,252

Difficulty

10.845465

Transactions

2

Size

3.16 KB

Version

2

Bits

0ad87064

Nonce

299,813,652

Timestamp

4/6/2017, 7:30:15 PM

Confirmations

4,768,106

Mined by

⛏️ P2SHAHBU9pBP8CRi8WaSFj5vQ5WH7zwyLMdWyZ

Merkle Root

f54789ad21ae865178db4fb4117bd403a23030bc8542f108a70a8a65723fa037
Transactions (2)
Coinbase3e2138445a729a…169570977a1abe
1 in β†’ 1 out8.5300 XPM109 B
AHBU9pBP…wyLMdWyZ
05f344df17eef6…6f1956464dc35e
20 in β†’ 2 out38.8335 XPM2.96 KB
AZrCy9M3…t8oTFdGAAKGxoSP8…8oH3hVLd
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.

2.678 Γ— 10⁹⁴(95-digit number)
26782203650695942534…58297227512344688639
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
2.678 Γ— 10⁹⁴(95-digit number)
26782203650695942534…58297227512344688639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.678 Γ— 10⁹⁴(95-digit number)
26782203650695942534…58297227512344688641
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
5.356 Γ— 10⁹⁴(95-digit number)
53564407301391885068…16594455024689377279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.356 Γ— 10⁹⁴(95-digit number)
53564407301391885068…16594455024689377281
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
1.071 Γ— 10⁹⁡(96-digit number)
10712881460278377013…33188910049378754559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.071 Γ— 10⁹⁡(96-digit number)
10712881460278377013…33188910049378754561
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
2.142 Γ— 10⁹⁡(96-digit number)
21425762920556754027…66377820098757509119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.142 Γ— 10⁹⁡(96-digit number)
21425762920556754027…66377820098757509121
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
4.285 Γ— 10⁹⁡(96-digit number)
42851525841113508054…32755640197515018239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.285 Γ— 10⁹⁡(96-digit number)
42851525841113508054…32755640197515018241
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
8.570 Γ— 10⁹⁡(96-digit number)
85703051682227016108…65511280395030036479
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
8.570 Γ— 10⁹⁡(96-digit number)
85703051682227016108…65511280395030036481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,862,963 XPMΒ·at block #6,827,357 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