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Block #659,385

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/2/2014, 2:13:33 PM Β· Difficulty 10.9562 Β· 6,147,514 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d1ca6eb1f73ba14e2094df89b4566344e70a02455cad49f3ae614843d931f3e1
View on Chainz β†—

Height

#659,385

Difficulty

10.956177

Transactions

2

Size

582 B

Version

2

Bits

0af4c800

Nonce

2,821,817,178

Timestamp

8/2/2014, 2:13:33 PM

Confirmations

6,147,514

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

40ad4cf3a231096189de37361f493da98a7d374848b9a7c04feb4bdc0d73e0f2
Transactions (2)
Coinbased8a49b9e6a5497…924d76dcd338d0
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
a7cd657eda33bc…1fb73d7b40205e
2 in β†’ 2 out10.3116 XPM376 B
AJNa2gH4…CWDfuxcnAZFyR8n4…Xiiavx12
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.

2.523 Γ— 10⁹⁡(96-digit number)
25231890731730470691…89988363017865867519
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
2.523 Γ— 10⁹⁡(96-digit number)
25231890731730470691…89988363017865867519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.523 Γ— 10⁹⁡(96-digit number)
25231890731730470691…89988363017865867521
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
5.046 Γ— 10⁹⁡(96-digit number)
50463781463460941383…79976726035731735039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.046 Γ— 10⁹⁡(96-digit number)
50463781463460941383…79976726035731735041
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
1.009 Γ— 10⁹⁢(97-digit number)
10092756292692188276…59953452071463470079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.009 Γ— 10⁹⁢(97-digit number)
10092756292692188276…59953452071463470081
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
2.018 Γ— 10⁹⁢(97-digit number)
20185512585384376553…19906904142926940159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.018 Γ— 10⁹⁢(97-digit number)
20185512585384376553…19906904142926940161
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
4.037 Γ— 10⁹⁢(97-digit number)
40371025170768753106…39813808285853880319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.037 Γ— 10⁹⁢(97-digit number)
40371025170768753106…39813808285853880321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
8.074 Γ— 10⁹⁢(97-digit number)
80742050341537506213…79627616571707760639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,699,301 XPMΒ·at block #6,806,898 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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