XPM Prime Explorer symbol
XPMPrime Explorer

Block #293,883

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/4/2013, 1:52:47 PM Β· Difficulty 9.9908 Β· 6,513,554 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
98bcd1fe06759befb4e067c04ad256493cc7e18e012ca1a03fa720543d06f755
View on Chainz β†—

Height

#293,883

Difficulty

9.990796

Transactions

1

Size

207 B

Version

2

Bits

09fda4d4

Nonce

335,546,937

Timestamp

12/4/2013, 1:52:47 PM

Confirmations

6,513,554

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

64e1138759642c39ff5a2d8b737a71ee6f2bbe2586d2ab5231d08345a81e19ab
Transactions (1)
Coinbase64e1138759642c…d08345a81e19ab
1 in β†’ 1 out10.0000 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.956 Γ— 10⁹⁢(97-digit number)
29564174292644576173…58950971739452124799
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
2.956 Γ— 10⁹⁢(97-digit number)
29564174292644576173…58950971739452124799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.956 Γ— 10⁹⁢(97-digit number)
29564174292644576173…58950971739452124801
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
5.912 Γ— 10⁹⁢(97-digit number)
59128348585289152346…17901943478904249599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.912 Γ— 10⁹⁢(97-digit number)
59128348585289152346…17901943478904249601
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
1.182 Γ— 10⁹⁷(98-digit number)
11825669717057830469…35803886957808499199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.182 Γ— 10⁹⁷(98-digit number)
11825669717057830469…35803886957808499201
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
2.365 Γ— 10⁹⁷(98-digit number)
23651339434115660938…71607773915616998399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.365 Γ— 10⁹⁷(98-digit number)
23651339434115660938…71607773915616998401
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
4.730 Γ— 10⁹⁷(98-digit number)
47302678868231321877…43215547831233996799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.730 Γ— 10⁹⁷(98-digit number)
47302678868231321877…43215547831233996801
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:57,703,518 XPMΒ·at block #6,807,436 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.
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