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Block #492,643

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/15/2014, 6:52:59 AM Β· Difficulty 10.6882 Β· 6,312,426 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ee46bafbf07bf83361502cb5182cc8a53db686fea246b24f99bec8dff12b6e46
View on Chainz β†—

Height

#492,643

Difficulty

10.688162

Transactions

3

Size

653 B

Version

2

Bits

0ab02b66

Nonce

21,877,335

Timestamp

4/15/2014, 6:52:59 AM

Confirmations

6,312,426

Mined by

⛏️ P2SHAY23ophy7HDAYCGevD3ovAJZFC8yoG9hfD

Merkle Root

655db818006a67bf4f69067392d56f4504bed5ae9cd29d80937753987cda4867
Transactions (3)
Coinbasebe20fa64e63f76…ce3092479fc7ca
1 in β†’ 1 out8.7600 XPM110 B
AY23ophy…8yoG9hfD
acdc978de614c9…817577b635785e
1 in β†’ 2 out10.0100 XPM226 B
AdX1oP8H…TMp4eTWmAQgVSsu2…PL9zdYUC
9b12085dad7f7a…857bd75c84a82d
1 in β†’ 2 out2.6225 XPM226 B
AXt3LRMi…kqpSSJoyAZTaiuc9…5hQfZCyt
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.

1.360 Γ— 10⁹⁢(97-digit number)
13600665436934517173…63119484498480092159
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
1.360 Γ— 10⁹⁢(97-digit number)
13600665436934517173…63119484498480092159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.360 Γ— 10⁹⁢(97-digit number)
13600665436934517173…63119484498480092161
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
2.720 Γ— 10⁹⁢(97-digit number)
27201330873869034347…26238968996960184319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.720 Γ— 10⁹⁢(97-digit number)
27201330873869034347…26238968996960184321
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
5.440 Γ— 10⁹⁢(97-digit number)
54402661747738068694…52477937993920368639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.440 Γ— 10⁹⁢(97-digit number)
54402661747738068694…52477937993920368641
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
1.088 Γ— 10⁹⁷(98-digit number)
10880532349547613738…04955875987840737279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.088 Γ— 10⁹⁷(98-digit number)
10880532349547613738…04955875987840737281
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
2.176 Γ— 10⁹⁷(98-digit number)
21761064699095227477…09911751975681474559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.176 Γ— 10⁹⁷(98-digit number)
21761064699095227477…09911751975681474561
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:57,684,618 XPMΒ·at block #6,805,068 Β· updates every 60s
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