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Block #667,002

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2014, 9:53:55 AM Β· Difficulty 10.9619 Β· 6,142,546 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a06a2b196e29ed5597c518bf3c5c6cbe3e1f125b8192043e4b17153b0b98bf52
View on Chainz β†—

Height

#667,002

Difficulty

10.961896

Transactions

2

Size

2.99 KB

Version

2

Bits

0af63ecd

Nonce

95,674,787

Timestamp

8/7/2014, 9:53:55 AM

Confirmations

6,142,546

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a8b07940462f4ba3d205ec79a5775052382cb753669907c56e186d9d15d95d24
Transactions (2)
Coinbase1b24d1b8cb615c…d3ac83a7398aa3
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
94fd81b994dd9f…183a41ef02ae3e
19 in β†’ 1 out54.9836 XPM2.79 KB
AVmMJWB2…zc5AYPpV
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.

2.042 Γ— 10⁹⁸(99-digit number)
20428737214238529911…34906511040732142719
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
2.042 Γ— 10⁹⁸(99-digit number)
20428737214238529911…34906511040732142719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.042 Γ— 10⁹⁸(99-digit number)
20428737214238529911…34906511040732142721
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
4.085 Γ— 10⁹⁸(99-digit number)
40857474428477059822…69813022081464285439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.085 Γ— 10⁹⁸(99-digit number)
40857474428477059822…69813022081464285441
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
8.171 Γ— 10⁹⁸(99-digit number)
81714948856954119645…39626044162928570879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.171 Γ— 10⁹⁸(99-digit number)
81714948856954119645…39626044162928570881
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
1.634 Γ— 10⁹⁹(100-digit number)
16342989771390823929…79252088325857141759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.634 Γ— 10⁹⁹(100-digit number)
16342989771390823929…79252088325857141761
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
3.268 Γ— 10⁹⁹(100-digit number)
32685979542781647858…58504176651714283519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.268 Γ— 10⁹⁹(100-digit number)
32685979542781647858…58504176651714283521
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:57,720,457 XPMΒ·at block #6,809,547 Β· updates every 60s
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