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Block #232,466

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/29/2013, 3:27:28 AM Β· Difficulty 9.9410 Β· 6,594,373 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5496f666df7b747a3e65649f8e3aa7245afe88421457536da186abca1109cc2a
View on Chainz β†—

Height

#232,466

Difficulty

9.941037

Transactions

1

Size

207 B

Version

2

Bits

09f0e7c8

Nonce

2,654

Timestamp

10/29/2013, 3:27:28 AM

Confirmations

6,594,373

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

f76988bcfdff3dfd4af2e8d28b8672d6ee7bb9779d0277fac52c4280b191deea
Transactions (1)
Coinbasef76988bcfdff3d…2c4280b191deea
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.

1.328 Γ— 10⁹⁢(97-digit number)
13282125689833355246…90895191409410883999
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
1.328 Γ— 10⁹⁢(97-digit number)
13282125689833355246…90895191409410883999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.328 Γ— 10⁹⁢(97-digit number)
13282125689833355246…90895191409410884001
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
2.656 Γ— 10⁹⁢(97-digit number)
26564251379666710492…81790382818821767999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.656 Γ— 10⁹⁢(97-digit number)
26564251379666710492…81790382818821768001
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
5.312 Γ— 10⁹⁢(97-digit number)
53128502759333420984…63580765637643535999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.312 Γ— 10⁹⁢(97-digit number)
53128502759333420984…63580765637643536001
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
1.062 Γ— 10⁹⁷(98-digit number)
10625700551866684196…27161531275287071999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.062 Γ— 10⁹⁷(98-digit number)
10625700551866684196…27161531275287072001
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
2.125 Γ— 10⁹⁷(98-digit number)
21251401103733368393…54323062550574143999
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:57,858,879 XPMΒ·at block #6,826,838 Β· updates every 60s
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