XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,416,487

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/17/2016, 2:16:24 AM Β· Difficulty 10.7949 Β· 5,393,368 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4efc5efccc50e29bc4a561ec69aafc007fba0f8017533704ca4d366c4632f07b
View on Chainz β†—

Height

#1,416,487

Difficulty

10.794928

Transactions

2

Size

12.25 KB

Version

2

Bits

0acb805f

Nonce

270,583,559

Timestamp

1/17/2016, 2:16:24 AM

Confirmations

5,393,368

Mined by

⛏️ P2SHAHbbw4CpapdxMqvwN2MegHipvFVspTXFS7

Merkle Root

379b3c78c03024d1ce26f492de2e92247e521431f09cac3579128b3c1d92d8f1
Transactions (2)
Coinbasea895a419af8684…b7f172985f0085
1 in β†’ 1 out8.7000 XPM110 B
AHbbw4Cp…VspTXFS7
95c91aac7c2da9…7e76533d49dc8e
83 in β†’ 2 out677.0775 XPM12.06 KB
AS9KDoJP…KyXLCdLYATJeka45…7yXJQkRn
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.

2.372 Γ— 10⁹⁴(95-digit number)
23727433843154243200…76574419096660774399
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
2.372 Γ— 10⁹⁴(95-digit number)
23727433843154243200…76574419096660774399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.372 Γ— 10⁹⁴(95-digit number)
23727433843154243200…76574419096660774401
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
4.745 Γ— 10⁹⁴(95-digit number)
47454867686308486401…53148838193321548799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.745 Γ— 10⁹⁴(95-digit number)
47454867686308486401…53148838193321548801
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
9.490 Γ— 10⁹⁴(95-digit number)
94909735372616972803…06297676386643097599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.490 Γ— 10⁹⁴(95-digit number)
94909735372616972803…06297676386643097601
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
1.898 Γ— 10⁹⁡(96-digit number)
18981947074523394560…12595352773286195199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.898 Γ— 10⁹⁡(96-digit number)
18981947074523394560…12595352773286195201
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
3.796 Γ— 10⁹⁡(96-digit number)
37963894149046789121…25190705546572390399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.796 Γ— 10⁹⁡(96-digit number)
37963894149046789121…25190705546572390401
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:57,722,927 XPMΒ·at block #6,809,854 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