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Block #531,135

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/8/2014, 7:47:38 AM Β· Difficulty 10.8935 Β· 6,274,930 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
064cce8405fdb5cdabd0d8a9c2786c5074abaa1a68389fb36c1f4b00f302fcf8
View on Chainz β†—

Height

#531,135

Difficulty

10.893455

Transactions

1

Size

208 B

Version

2

Bits

0ae4b97a

Nonce

22,108,247

Timestamp

5/8/2014, 7:47:38 AM

Confirmations

6,274,930

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

058cb9a6110013d802dc0eb75dd71d5f4ff8771f4a44f2960e1ff60522ae19d1
Transactions (1)
Coinbase058cb9a6110013…1ff60522ae19d1
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

9.473 Γ— 10⁹⁹(100-digit number)
94736857625120253277…19766092212677830399
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
9.473 Γ— 10⁹⁹(100-digit number)
94736857625120253277…19766092212677830399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.473 Γ— 10⁹⁹(100-digit number)
94736857625120253277…19766092212677830401
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
1.894 Γ— 10¹⁰⁰(101-digit number)
18947371525024050655…39532184425355660799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.894 Γ— 10¹⁰⁰(101-digit number)
18947371525024050655…39532184425355660801
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
3.789 Γ— 10¹⁰⁰(101-digit number)
37894743050048101311…79064368850711321599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.789 Γ— 10¹⁰⁰(101-digit number)
37894743050048101311…79064368850711321601
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
7.578 Γ— 10¹⁰⁰(101-digit number)
75789486100096202622…58128737701422643199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.578 Γ— 10¹⁰⁰(101-digit number)
75789486100096202622…58128737701422643201
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
1.515 Γ— 10¹⁰¹(102-digit number)
15157897220019240524…16257475402845286399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.515 Γ— 10¹⁰¹(102-digit number)
15157897220019240524…16257475402845286401
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
3.031 Γ— 10¹⁰¹(102-digit number)
30315794440038481048…32514950805690572799
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:57,692,604 XPMΒ·at block #6,806,064 Β· updates every 60s
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