XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,294,303

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2017, 5:56:24 AM Β· Difficulty 10.9529 Β· 4,550,395 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
10adaae555136c3e8e753a22ef58ed1b0792cdb0a7db1679cc536d47e6b2e175
View on Chainz β†—

Height

#2,294,303

Difficulty

10.952890

Transactions

1

Size

200 B

Version

2

Bits

0af3f09e

Nonce

341,737,188

Timestamp

9/13/2017, 5:56:24 AM

Confirmations

4,550,395

Mined by

⛏️ P2SHAX5bP8Yife1KAodFLnoECyTcW3gYGdBXVA

Merkle Root

4e685ab83598808cadeb1fb34c2a7de6337daf6f554c679ad868c86f106d89f9
Transactions (1)
Coinbase4e685ab8359880…68c86f106d89f9
1 in β†’ 1 out8.3200 XPM110 B
AX5bP8Yi…gYGdBXVA
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.

9.419 Γ— 10⁹⁴(95-digit number)
94199832075014828899…04165899559206238719
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
9.419 Γ— 10⁹⁴(95-digit number)
94199832075014828899…04165899559206238719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.419 Γ— 10⁹⁴(95-digit number)
94199832075014828899…04165899559206238721
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
1.883 Γ— 10⁹⁡(96-digit number)
18839966415002965779…08331799118412477439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.883 Γ— 10⁹⁡(96-digit number)
18839966415002965779…08331799118412477441
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
3.767 Γ— 10⁹⁡(96-digit number)
37679932830005931559…16663598236824954879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.767 Γ— 10⁹⁡(96-digit number)
37679932830005931559…16663598236824954881
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
7.535 Γ— 10⁹⁡(96-digit number)
75359865660011863119…33327196473649909759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.535 Γ— 10⁹⁡(96-digit number)
75359865660011863119…33327196473649909761
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
1.507 Γ— 10⁹⁢(97-digit number)
15071973132002372623…66654392947299819519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.507 Γ— 10⁹⁢(97-digit number)
15071973132002372623…66654392947299819521
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
3.014 Γ— 10⁹⁢(97-digit number)
30143946264004745247…33308785894599639039
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:58,001,994 XPMΒ·at block #6,844,697 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