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Block #519,500

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2014, 6:48:29 AM Β· Difficulty 10.8560 Β· 6,296,380 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a6cb6a8d1bb816993d653c5c19192a78ecb34554e18f073bcb313de664435b01
View on Chainz β†—

Height

#519,500

Difficulty

10.855994

Transactions

2

Size

427 B

Version

2

Bits

0adb226e

Nonce

455,160

Timestamp

5/1/2014, 6:48:29 AM

Confirmations

6,296,380

Mined by

⛏️ P2SHAWN1nToNZEtgCe4iRMyiJE3dNyxZHJj3Fm

Merkle Root

aed20fd9f51cf74c52708b9919ba0e7604efa15fabdacf8f74b14b613515d3ce
Transactions (2)
Coinbase3e98d1f2bbf622…511faea8ec8243
1 in β†’ 1 out8.4800 XPM110 B
AWN1nToN…xZHJj3Fm
2e34100ce229a6…25621fa87563b6
1 in β†’ 2 out8.4800 XPM226 B
AGRrLX34…F9zbreReAaUUYySJ…Dq99Mmwq
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.

4.635 Γ— 10⁹⁢(97-digit number)
46351327453998521636…67761866085699059359
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
4.635 Γ— 10⁹⁢(97-digit number)
46351327453998521636…67761866085699059359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.635 Γ— 10⁹⁢(97-digit number)
46351327453998521636…67761866085699059361
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
9.270 Γ— 10⁹⁢(97-digit number)
92702654907997043272…35523732171398118719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.270 Γ— 10⁹⁢(97-digit number)
92702654907997043272…35523732171398118721
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
1.854 Γ— 10⁹⁷(98-digit number)
18540530981599408654…71047464342796237439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.854 Γ— 10⁹⁷(98-digit number)
18540530981599408654…71047464342796237441
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
3.708 Γ— 10⁹⁷(98-digit number)
37081061963198817309…42094928685592474879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.708 Γ— 10⁹⁷(98-digit number)
37081061963198817309…42094928685592474881
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
7.416 Γ— 10⁹⁷(98-digit number)
74162123926397634618…84189857371184949759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.416 Γ— 10⁹⁷(98-digit number)
74162123926397634618…84189857371184949761
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:57,771,153 XPMΒ·at block #6,815,879 Β· updates every 60s
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