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Block #1,411,863

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/13/2016, 5:04:22 PM Β· Difficulty 10.8048 Β· 5,402,619 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b3b93df36e75c5d0c386e41e3d31d1a62ca8890f6bfb4b34f98f726481def364
View on Chainz β†—

Height

#1,411,863

Difficulty

10.804761

Transactions

2

Size

3.75 KB

Version

2

Bits

0ace04cf

Nonce

254,499,510

Timestamp

1/13/2016, 5:04:22 PM

Confirmations

5,402,619

Mined by

⛏️ P2SHATmntS7pYJoBe5WicjKAjkLi5omQeV3qAr

Merkle Root

76ed4137ef1c9af8cd5fd110ce3d290701a186d53a177220f02363940a61e231
Transactions (2)
Coinbaseb2f546e32cc2c4…28d6dc7e90577d
1 in β†’ 1 out8.5900 XPM110 B
ATmntS7p…mQeV3qAr
77971c8b5c5095…0360eee99c8d7c
24 in β†’ 2 out119.7600 XPM3.55 KB
AST3A6TH…ZNsyjNeYATJT1Fh6…TT94HidZ
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.

1.389 Γ— 10⁹⁡(96-digit number)
13895966200495534828…14886289862512288319
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
1.389 Γ— 10⁹⁡(96-digit number)
13895966200495534828…14886289862512288319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.389 Γ— 10⁹⁡(96-digit number)
13895966200495534828…14886289862512288321
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
2.779 Γ— 10⁹⁡(96-digit number)
27791932400991069657…29772579725024576639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.779 Γ— 10⁹⁡(96-digit number)
27791932400991069657…29772579725024576641
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
5.558 Γ— 10⁹⁡(96-digit number)
55583864801982139315…59545159450049153279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.558 Γ— 10⁹⁡(96-digit number)
55583864801982139315…59545159450049153281
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
1.111 Γ— 10⁹⁢(97-digit number)
11116772960396427863…19090318900098306559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.111 Γ— 10⁹⁢(97-digit number)
11116772960396427863…19090318900098306561
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
2.223 Γ— 10⁹⁢(97-digit number)
22233545920792855726…38180637800196613119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.223 Γ— 10⁹⁢(97-digit number)
22233545920792855726…38180637800196613121
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:57,759,932 XPMΒ·at block #6,814,481 Β· updates every 60s
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