XPM Prime Explorer symbol
XPMPrime Explorer

Block #151,835

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2013, 10:16:51 PM Β· Difficulty 9.8620 Β· 6,648,833 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f18d3b020e5dfd7c7552f050168ed836aad9bff52fbc83983cf9c54da570e84c
View on Chainz β†—

Height

#151,835

Difficulty

9.862018

Transactions

1

Size

197 B

Version

2

Bits

09dcad35

Nonce

155,201

Timestamp

9/5/2013, 10:16:51 PM

Confirmations

6,648,833

Mined by

⛏️ P2SHAa6PpN3XWen9U28VLp3hDw33d6XAm9RHxt

Merkle Root

b960127bee22e6246c5f9c54b2e4944c1b84967529d2121d146eb2aca84b8bf1
Transactions (1)
Coinbaseb960127bee22e6…6eb2aca84b8bf1
1 in β†’ 1 out10.2700 XPM109 B
Aa6PpN3X…XAm9RHxt
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.

2.035 Γ— 10⁸⁹(90-digit number)
20355158989618632152…43039681710280046579
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
2.035 Γ— 10⁸⁹(90-digit number)
20355158989618632152…43039681710280046579
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.035 Γ— 10⁸⁹(90-digit number)
20355158989618632152…43039681710280046581
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
4.071 Γ— 10⁸⁹(90-digit number)
40710317979237264304…86079363420560093159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.071 Γ— 10⁸⁹(90-digit number)
40710317979237264304…86079363420560093161
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
8.142 Γ— 10⁸⁹(90-digit number)
81420635958474528609…72158726841120186319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.142 Γ— 10⁸⁹(90-digit number)
81420635958474528609…72158726841120186321
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
1.628 Γ— 10⁹⁰(91-digit number)
16284127191694905721…44317453682240372639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.628 Γ— 10⁹⁰(91-digit number)
16284127191694905721…44317453682240372641
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
3.256 Γ— 10⁹⁰(91-digit number)
32568254383389811443…88634907364480745279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,649,407 XPMΒ·at block #6,800,667 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