XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,098,299

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2017, 11:42:23 AM Β· Difficulty 10.8651 Β· 4,718,143 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1051807cba493b6a15e085df1c01c51a6f1c66fbc8f08752e18cab20dba21874
View on Chainz β†—

Height

#2,098,299

Difficulty

10.865121

Transactions

2

Size

14.59 KB

Version

2

Bits

0add7898

Nonce

1,011,326,533

Timestamp

5/3/2017, 11:42:23 AM

Confirmations

4,718,143

Mined by

⛏️ P2SHAHRwLdTsuriFCUZNik1LEjXjHKkUuwQeDJ

Merkle Root

dc868e46ed84342479cbcbfd83d2aae4278d624dc1bb9680d6c3a6ab0cf8bb18
Transactions (2)
Coinbase20faab772a6a8b…6e1e602c2ba3d1
1 in β†’ 1 out8.6600 XPM110 B
AHRwLdTs…kUuwQeDJ
451e71ca44beb5…a5a33138410fc5
99 in β†’ 2 out3.5802 XPM14.40 KB
AK8YfSLc…wDng27bgAKGxoSP8…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.

1.777 Γ— 10⁹⁴(95-digit number)
17770297106315959082…52470952272528349399
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
1.777 Γ— 10⁹⁴(95-digit number)
17770297106315959082…52470952272528349399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.777 Γ— 10⁹⁴(95-digit number)
17770297106315959082…52470952272528349401
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
3.554 Γ— 10⁹⁴(95-digit number)
35540594212631918164…04941904545056698799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.554 Γ— 10⁹⁴(95-digit number)
35540594212631918164…04941904545056698801
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
7.108 Γ— 10⁹⁴(95-digit number)
71081188425263836328…09883809090113397599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.108 Γ— 10⁹⁴(95-digit number)
71081188425263836328…09883809090113397601
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
1.421 Γ— 10⁹⁡(96-digit number)
14216237685052767265…19767618180226795199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.421 Γ— 10⁹⁡(96-digit number)
14216237685052767265…19767618180226795201
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
2.843 Γ— 10⁹⁡(96-digit number)
28432475370105534531…39535236360453590399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.843 Γ— 10⁹⁡(96-digit number)
28432475370105534531…39535236360453590401
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:57,775,662 XPMΒ·at block #6,816,441 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