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Block #588,803

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/14/2014, 11:09:46 PM Β· Difficulty 10.9488 Β· 6,220,296 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1fcfe935defce222582a38c183bc64c245f3850fe0bf4dbc851c726479f179b3
View on Chainz β†—

Height

#588,803

Difficulty

10.948753

Transactions

1

Size

243 B

Version

2

Bits

0af2e177

Nonce

942,779,150

Timestamp

6/14/2014, 11:09:46 PM

Confirmations

6,220,296

Mined by

⛏️ P2SHAXn1KW6PTFKBcGVcbZ8CPoUc4Pc7VDu2zv

Merkle Root

9e8e6135dcfba6bff312de0b05916b4c9c47e3213781e3dea341f9ccdcfdab1e
Transactions (1)
Coinbase9e8e6135dcfba6…41f9ccdcfdab1e
1 in β†’ 2 out8.3300 XPM152 B
AXn1KW6P…c7VDu2zvALPu3s2c…EJXLjVFh
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.

2.229 Γ— 10⁹⁸(99-digit number)
22299199328798739187…96334864590696444159
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
2.229 Γ— 10⁹⁸(99-digit number)
22299199328798739187…96334864590696444159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.229 Γ— 10⁹⁸(99-digit number)
22299199328798739187…96334864590696444161
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
4.459 Γ— 10⁹⁸(99-digit number)
44598398657597478374…92669729181392888319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.459 Γ— 10⁹⁸(99-digit number)
44598398657597478374…92669729181392888321
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
8.919 Γ— 10⁹⁸(99-digit number)
89196797315194956748…85339458362785776639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.919 Γ— 10⁹⁸(99-digit number)
89196797315194956748…85339458362785776641
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
1.783 Γ— 10⁹⁹(100-digit number)
17839359463038991349…70678916725571553279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.783 Γ— 10⁹⁹(100-digit number)
17839359463038991349…70678916725571553281
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
3.567 Γ— 10⁹⁹(100-digit number)
35678718926077982699…41357833451143106559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.567 Γ— 10⁹⁹(100-digit number)
35678718926077982699…41357833451143106561
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:57,716,846 XPMΒ·at block #6,809,098 Β· updates every 60s
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