XPM Prime Explorer symbol
XPMPrime Explorer

Block #131,875

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/24/2013, 2:01:55 PM Β· Difficulty 9.7860 Β· 6,682,256 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fd8c71807a8a0faa65b4e734510bf99a94bf31db9a6091f4c01383962132ba07
View on Chainz β†—

Height

#131,875

Difficulty

9.786050

Transactions

1

Size

203 B

Version

2

Bits

09c93a8b

Nonce

6,131

Timestamp

8/24/2013, 2:01:55 PM

Confirmations

6,682,256

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

8b9dcf875a16bd5c80ab7a2a7f0b6b8970704d23be4e1dedaaf2076a47026ae5
Transactions (1)
Coinbase8b9dcf875a16bd…f2076a47026ae5
1 in β†’ 1 out10.4300 XPM112 B
AT5A2KL6…CT16n6i2
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.

4.580 Γ— 10⁹⁢(97-digit number)
45805061332941520126…19105615350478218879
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
4.580 Γ— 10⁹⁢(97-digit number)
45805061332941520126…19105615350478218879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.580 Γ— 10⁹⁢(97-digit number)
45805061332941520126…19105615350478218881
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
9.161 Γ— 10⁹⁢(97-digit number)
91610122665883040252…38211230700956437759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.161 Γ— 10⁹⁢(97-digit number)
91610122665883040252…38211230700956437761
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
1.832 Γ— 10⁹⁷(98-digit number)
18322024533176608050…76422461401912875519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.832 Γ— 10⁹⁷(98-digit number)
18322024533176608050…76422461401912875521
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
3.664 Γ— 10⁹⁷(98-digit number)
36644049066353216100…52844922803825751039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.664 Γ— 10⁹⁷(98-digit number)
36644049066353216100…52844922803825751041
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
7.328 Γ— 10⁹⁷(98-digit number)
73288098132706432201…05689845607651502079
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:57,757,131 XPMΒ·at block #6,814,130 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