XPM Prime Explorer symbol
XPMPrime Explorer

Block #76,575

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/22/2013, 2:02:28 AM Β· Difficulty 9.1078 Β· 6,733,394 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d123ab015b2e0680fcd0c84bd43899790c4d0ab6ba5da1601a08a9149183c9b5
View on Chainz β†—

Height

#76,575

Difficulty

9.107846

Transactions

1

Size

202 B

Version

2

Bits

091b9bc8

Nonce

36

Timestamp

7/22/2013, 2:02:28 AM

Confirmations

6,733,394

Mined by

⛏️ P2SHANey87HKeHbF7P31ach44cVFqNMGUx5bYr

Merkle Root

2f857fe680cc29c1c904992516132087ec6052c3e8c65132c29111e6ec180ea2
Transactions (1)
Coinbase2f857fe680cc29…9111e6ec180ea2
1 in β†’ 1 out12.0400 XPM110 B
ANey87HK…MGUx5bYr
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.

1.005 Γ— 10¹⁰⁰(101-digit number)
10057945097070734999…37126290608338415719
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
1.005 Γ— 10¹⁰⁰(101-digit number)
10057945097070734999…37126290608338415719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.005 Γ— 10¹⁰⁰(101-digit number)
10057945097070734999…37126290608338415721
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
2.011 Γ— 10¹⁰⁰(101-digit number)
20115890194141469998…74252581216676831439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.011 Γ— 10¹⁰⁰(101-digit number)
20115890194141469998…74252581216676831441
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
4.023 Γ— 10¹⁰⁰(101-digit number)
40231780388282939997…48505162433353662879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.023 Γ— 10¹⁰⁰(101-digit number)
40231780388282939997…48505162433353662881
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
8.046 Γ— 10¹⁰⁰(101-digit number)
80463560776565879995…97010324866707325759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.046 Γ— 10¹⁰⁰(101-digit number)
80463560776565879995…97010324866707325761
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
1.609 Γ— 10¹⁰¹(102-digit number)
16092712155313175999…94020649733414651519
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:57,723,825 XPMΒ·at block #6,809,968 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