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Block #175,529

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/22/2013, 8:58:04 AM Β· Difficulty 9.8636 Β· 6,632,537 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2e609590c58ba3668016ad5021c16b8651887cfa9b95bcdb6391ff7046fb6ee4
View on Chainz β†—

Height

#175,529

Difficulty

9.863557

Transactions

1

Size

200 B

Version

2

Bits

09dd1216

Nonce

104,827

Timestamp

9/22/2013, 8:58:04 AM

Confirmations

6,632,537

Mined by

⛏️ P2SHAR5gyTZNg6ZeNPiKvdEqxhmWsGE6QBE8y6

Merkle Root

f2b3919a276e87e6e6f94fa64dee6b5f5f3aeec12054227e88c963a57efd9a5c
Transactions (1)
Coinbasef2b3919a276e87…c963a57efd9a5c
1 in β†’ 1 out10.2600 XPM109 B
AR5gyTZN…E6QBE8y6
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.

1.632 Γ— 10⁹⁢(97-digit number)
16327855027690161088…96910749894683039839
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
1.632 Γ— 10⁹⁢(97-digit number)
16327855027690161088…96910749894683039839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.632 Γ— 10⁹⁢(97-digit number)
16327855027690161088…96910749894683039841
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
3.265 Γ— 10⁹⁢(97-digit number)
32655710055380322177…93821499789366079679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.265 Γ— 10⁹⁢(97-digit number)
32655710055380322177…93821499789366079681
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
6.531 Γ— 10⁹⁢(97-digit number)
65311420110760644355…87642999578732159359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.531 Γ— 10⁹⁢(97-digit number)
65311420110760644355…87642999578732159361
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
1.306 Γ— 10⁹⁷(98-digit number)
13062284022152128871…75285999157464318719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.306 Γ— 10⁹⁷(98-digit number)
13062284022152128871…75285999157464318721
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
2.612 Γ— 10⁹⁷(98-digit number)
26124568044304257742…50571998314928637439
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:57,708,573 XPMΒ·at block #6,808,065 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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