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Block #235,530

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2013, 11:33:16 PM Β· Difficulty 9.9459 Β· 6,570,753 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8a1997451238c7daa1e9112b5f58c0153827772a7366b3f25863021652a11fa7
View on Chainz β†—

Height

#235,530

Difficulty

9.945861

Transactions

1

Size

198 B

Version

2

Bits

09f223ef

Nonce

242,589

Timestamp

10/30/2013, 11:33:16 PM

Confirmations

6,570,753

Mined by

⛏️ P2SHAPpAmzuiarcDRTEE9yddUu8j7EbKYJJ5pB

Merkle Root

9c5efa5251d05b15cedb48b36177c5dac6dff81e64181816b6377967c8d8411e
Transactions (1)
Coinbase9c5efa5251d05b…377967c8d8411e
1 in β†’ 1 out10.0900 XPM109 B
APpAmzui…bKYJJ5pB
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.

2.161 Γ— 10⁹²(93-digit number)
21619443805080801429…42257479356203979679
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
2.161 Γ— 10⁹²(93-digit number)
21619443805080801429…42257479356203979679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.161 Γ— 10⁹²(93-digit number)
21619443805080801429…42257479356203979681
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
4.323 Γ— 10⁹²(93-digit number)
43238887610161602858…84514958712407959359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.323 Γ— 10⁹²(93-digit number)
43238887610161602858…84514958712407959361
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
8.647 Γ— 10⁹²(93-digit number)
86477775220323205716…69029917424815918719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.647 Γ— 10⁹²(93-digit number)
86477775220323205716…69029917424815918721
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
1.729 Γ— 10⁹³(94-digit number)
17295555044064641143…38059834849631837439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.729 Γ— 10⁹³(94-digit number)
17295555044064641143…38059834849631837441
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
3.459 Γ— 10⁹³(94-digit number)
34591110088129282286…76119669699263674879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,694,350 XPMΒ·at block #6,806,282 Β· updates every 60s
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