XPM Prime Explorer symbol
XPMPrime Explorer

Block #260,307

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/14/2013, 4:27:08 AM Β· Difficulty 9.9777 Β· 6,543,297 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4b1364d3f02587cd34b611d5bcb0dda226dab1ad7b203dd498618eeba6efb310
View on Chainz β†—

Height

#260,307

Difficulty

9.977661

Transactions

1

Size

198 B

Version

2

Bits

09fa47ff

Nonce

107,232

Timestamp

11/14/2013, 4:27:08 AM

Confirmations

6,543,297

Mined by

⛏️ P2SHARBRYiL8QjnU5zrwTmS3JgwVXJoj38gY3N

Merkle Root

5e0c98d08a4ef5935c72053113095bc776ec3079ebfbcb1cede5b389d0164f71
Transactions (1)
Coinbase5e0c98d08a4ef5…e5b389d0164f71
1 in β†’ 1 out10.0300 XPM109 B
ARBRYiL8…oj38gY3N
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.

2.180 Γ— 10⁹³(94-digit number)
21806124639296179276…50880924463161183359
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
2.180 Γ— 10⁹³(94-digit number)
21806124639296179276…50880924463161183359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.180 Γ— 10⁹³(94-digit number)
21806124639296179276…50880924463161183361
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
4.361 Γ— 10⁹³(94-digit number)
43612249278592358553…01761848926322366719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.361 Γ— 10⁹³(94-digit number)
43612249278592358553…01761848926322366721
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
8.722 Γ— 10⁹³(94-digit number)
87224498557184717107…03523697852644733439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.722 Γ— 10⁹³(94-digit number)
87224498557184717107…03523697852644733441
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
1.744 Γ— 10⁹⁴(95-digit number)
17444899711436943421…07047395705289466879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.744 Γ— 10⁹⁴(95-digit number)
17444899711436943421…07047395705289466881
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
3.488 Γ— 10⁹⁴(95-digit number)
34889799422873886842…14094791410578933759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.488 Γ— 10⁹⁴(95-digit number)
34889799422873886842…14094791410578933761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,672,871 XPMΒ·at block #6,803,603 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