XPM Prime Explorer symbol
XPMPrime Explorer

Block #44,807

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2013, 12:47:12 AM Β· Difficulty 8.7316 Β· 6,767,791 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3ee42ac0889dbe345cf50f1d2052ce9d0f98da27d089107af4528ad5c5ec124c
View on Chainz β†—

Height

#44,807

Difficulty

8.731635

Transactions

1

Size

199 B

Version

2

Bits

08bb4c68

Nonce

1,011

Timestamp

7/15/2013, 12:47:12 AM

Confirmations

6,767,791

Mined by

⛏️ P2SHAWeEPkwufuUheXG36vmXaEF2nt2eMpSWHE

Merkle Root

27f9a51d700cd56a0aff19a66e285f88c837c17b4225c674aebb209e3a685890
Transactions (1)
Coinbase27f9a51d700cd5…bb209e3a685890
1 in β†’ 1 out13.1000 XPM110 B
AWeEPkwu…2eMpSWHE
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.

7.857 Γ— 10⁹¹(92-digit number)
78578249278129324003…10981695274143650519
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
7.857 Γ— 10⁹¹(92-digit number)
78578249278129324003…10981695274143650519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.857 Γ— 10⁹¹(92-digit number)
78578249278129324003…10981695274143650521
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
1.571 Γ— 10⁹²(93-digit number)
15715649855625864800…21963390548287301039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.571 Γ— 10⁹²(93-digit number)
15715649855625864800…21963390548287301041
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
3.143 Γ— 10⁹²(93-digit number)
31431299711251729601…43926781096574602079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.143 Γ— 10⁹²(93-digit number)
31431299711251729601…43926781096574602081
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
6.286 Γ— 10⁹²(93-digit number)
62862599422503459203…87853562193149204159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.286 Γ— 10⁹²(93-digit number)
62862599422503459203…87853562193149204161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,744,819 XPMΒ·at block #6,812,597 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