XPM Prime Explorer symbol
XPMPrime Explorer

Block #31,849

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 12:55:52 AM Β· Difficulty 7.9894 Β· 6,795,381 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
af7353519d9d1696fc3b321c63b6dd47a94eb278d34c6e0d7d61d062a1ad953f
View on Chainz β†—

Height

#31,849

Difficulty

7.989400

Transactions

1

Size

197 B

Version

2

Bits

07fd4952

Nonce

416

Timestamp

7/14/2013, 12:55:52 AM

Confirmations

6,795,381

Mined by

⛏️ P2SHAedCo1qGFPkcqJFcCvRmpjxjtczFAZ1w75

Merkle Root

8731417629e46116322d579d87243c9a99a6af8df0e8aed6203cb637dfdaf8bb
Transactions (1)
Coinbase8731417629e461…3cb637dfdaf8bb
1 in β†’ 1 out15.6500 XPM108 B
AedCo1qG…zFAZ1w75
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.

2.033 Γ— 10⁹³(94-digit number)
20337381424003912081…35851053810912491599
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
2.033 Γ— 10⁹³(94-digit number)
20337381424003912081…35851053810912491599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.033 Γ— 10⁹³(94-digit number)
20337381424003912081…35851053810912491601
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
4.067 Γ— 10⁹³(94-digit number)
40674762848007824163…71702107621824983199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.067 Γ— 10⁹³(94-digit number)
40674762848007824163…71702107621824983201
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
8.134 Γ— 10⁹³(94-digit number)
81349525696015648327…43404215243649966399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.134 Γ— 10⁹³(94-digit number)
81349525696015648327…43404215243649966401
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
1.626 Γ— 10⁹⁴(95-digit number)
16269905139203129665…86808430487299932799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,861,940 XPMΒ·at block #6,827,229 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