XPM Prime Explorer symbol
XPMPrime Explorer

Block #663,521

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/5/2014, 8:32:00 AM Β· Difficulty 10.9577 Β· 6,152,276 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
72266a42ac549507c98d4e8a66a832d41d4ee2f2c5e0776baa6fd7a38b01c3e8
View on Chainz β†—

Height

#663,521

Difficulty

10.957654

Transactions

2

Size

27.61 KB

Version

2

Bits

0af528d5

Nonce

1,238,168,028

Timestamp

8/5/2014, 8:32:00 AM

Confirmations

6,152,276

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7d7814ad315502a481a52287d58c2cf0662e9d52a7b0c68a2390b03281f4b4a0
Transactions (2)
Coinbasec863779740b2a5…dfa0f3b7af28bd
1 in β†’ 1 out8.6100 XPM116 B
ANSXnLY2…Sd25TjkD
1231386f9d5199…648aa9f765587f
189 in β†’ 2 out424.0153 XPM27.41 KB
AV4Xnr9r…FWx4wj5FANmk3NFG…zNV2Y89D
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.

2.230 Γ— 10⁹⁸(99-digit number)
22307497295784433820…73207543431073791999
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
2.230 Γ— 10⁹⁸(99-digit number)
22307497295784433820…73207543431073791999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.230 Γ— 10⁹⁸(99-digit number)
22307497295784433820…73207543431073792001
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
4.461 Γ— 10⁹⁸(99-digit number)
44614994591568867640…46415086862147583999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.461 Γ— 10⁹⁸(99-digit number)
44614994591568867640…46415086862147584001
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
8.922 Γ— 10⁹⁸(99-digit number)
89229989183137735280…92830173724295167999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.922 Γ— 10⁹⁸(99-digit number)
89229989183137735280…92830173724295168001
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
1.784 Γ— 10⁹⁹(100-digit number)
17845997836627547056…85660347448590335999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.784 Γ— 10⁹⁹(100-digit number)
17845997836627547056…85660347448590336001
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
3.569 Γ— 10⁹⁹(100-digit number)
35691995673255094112…71320694897180671999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.569 Γ— 10⁹⁹(100-digit number)
35691995673255094112…71320694897180672001
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
7.138 Γ— 10⁹⁹(100-digit number)
71383991346510188224…42641389794361343999
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:57,770,480 XPMΒ·at block #6,815,796 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