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Block #232,601

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/29/2013, 5:24:06 AM Β· Difficulty 9.9413 Β· 6,609,756 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4496267ef87cad16ffd28594ac7a9c33373043691e73c9b06e5cdf2d129eb15b
View on Chainz β†—

Height

#232,601

Difficulty

9.941276

Transactions

1

Size

207 B

Version

2

Bits

09f0f77f

Nonce

523,970

Timestamp

10/29/2013, 5:24:06 AM

Confirmations

6,609,756

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

cb6f914e9d299b7349a674d38750752dc5055059b8bd2c0a107a86f810ca0125
Transactions (1)
Coinbasecb6f914e9d299b…7a86f810ca0125
1 in β†’ 1 out10.1000 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.402 Γ— 10⁹⁸(99-digit number)
14023285749419865029…86981210570755568059
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
1.402 Γ— 10⁹⁸(99-digit number)
14023285749419865029…86981210570755568059
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.402 Γ— 10⁹⁸(99-digit number)
14023285749419865029…86981210570755568061
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
2.804 Γ— 10⁹⁸(99-digit number)
28046571498839730059…73962421141511136119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.804 Γ— 10⁹⁸(99-digit number)
28046571498839730059…73962421141511136121
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
5.609 Γ— 10⁹⁸(99-digit number)
56093142997679460118…47924842283022272239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.609 Γ— 10⁹⁸(99-digit number)
56093142997679460118…47924842283022272241
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
1.121 Γ— 10⁹⁹(100-digit number)
11218628599535892023…95849684566044544479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.121 Γ— 10⁹⁹(100-digit number)
11218628599535892023…95849684566044544481
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
2.243 Γ— 10⁹⁹(100-digit number)
22437257199071784047…91699369132089088959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.243 Γ— 10⁹⁹(100-digit number)
22437257199071784047…91699369132089088961
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:57,983,263 XPMΒ·at block #6,842,356 Β· updates every 60s
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