XPM Prime Explorer symbol
XPMPrime Explorer

Block #84,857

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2013, 2:26:35 AM Β· Difficulty 9.2775 Β· 6,717,733 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
882292c62a65accefa6bcc1853ed48985c70dfe58024e6fdff3af90b7424e530
View on Chainz β†—

Height

#84,857

Difficulty

9.277544

Transactions

1

Size

204 B

Version

2

Bits

09470d20

Nonce

77,985

Timestamp

7/27/2013, 2:26:35 AM

Confirmations

6,717,733

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

9da3f91c204757f1499b695ccd12829b526656c3a7d1002fb1d1766259c40bf1
Transactions (1)
Coinbase9da3f91c204757…d1766259c40bf1
1 in β†’ 1 out11.6000 XPM109 B
ATe7tG7X…yczDSDEp
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.

3.045 Γ— 10¹⁰⁷(108-digit number)
30455151578620210084…48113358207800423399
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
3.045 Γ— 10¹⁰⁷(108-digit number)
30455151578620210084…48113358207800423399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.045 Γ— 10¹⁰⁷(108-digit number)
30455151578620210084…48113358207800423401
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
6.091 Γ— 10¹⁰⁷(108-digit number)
60910303157240420168…96226716415600846799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.091 Γ— 10¹⁰⁷(108-digit number)
60910303157240420168…96226716415600846801
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
1.218 Γ— 10¹⁰⁸(109-digit number)
12182060631448084033…92453432831201693599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.218 Γ— 10¹⁰⁸(109-digit number)
12182060631448084033…92453432831201693601
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
2.436 Γ— 10¹⁰⁸(109-digit number)
24364121262896168067…84906865662403387199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.436 Γ— 10¹⁰⁸(109-digit number)
24364121262896168067…84906865662403387201
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
4.872 Γ— 10¹⁰⁸(109-digit number)
48728242525792336135…69813731324806774399
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:57,664,738 XPMΒ·at block #6,802,589 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