XPM Prime Explorer symbol
XPMPrime Explorer

Block #567,371

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2014, 4:40:00 PM Β· Difficulty 10.9649 Β· 6,259,859 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
853ffad02ca4ad5dd4891798a0bd81abacfa17aa55449ceecce96686b3159cbe
View on Chainz β†—

Height

#567,371

Difficulty

10.964866

Transactions

1

Size

207 B

Version

2

Bits

0af7016f

Nonce

21,289,159

Timestamp

5/29/2014, 4:40:00 PM

Confirmations

6,259,859

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

58d9593ffac75ff381131b138b4a2eb0c398c9ecb5e5ccd95d31a1675ce6fafc
Transactions (1)
Coinbase58d9593ffac75f…31a1675ce6fafc
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.377 Γ— 10⁹⁷(98-digit number)
33778400443125692234…11889929782419144639
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
3.377 Γ— 10⁹⁷(98-digit number)
33778400443125692234…11889929782419144639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.377 Γ— 10⁹⁷(98-digit number)
33778400443125692234…11889929782419144641
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
6.755 Γ— 10⁹⁷(98-digit number)
67556800886251384469…23779859564838289279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.755 Γ— 10⁹⁷(98-digit number)
67556800886251384469…23779859564838289281
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
1.351 Γ— 10⁹⁸(99-digit number)
13511360177250276893…47559719129676578559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.351 Γ— 10⁹⁸(99-digit number)
13511360177250276893…47559719129676578561
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
2.702 Γ— 10⁹⁸(99-digit number)
27022720354500553787…95119438259353157119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.702 Γ— 10⁹⁸(99-digit number)
27022720354500553787…95119438259353157121
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
5.404 Γ— 10⁹⁸(99-digit number)
54045440709001107575…90238876518706314239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.404 Γ— 10⁹⁸(99-digit number)
54045440709001107575…90238876518706314241
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:57,861,940 XPMΒ·at block #6,827,229 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