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Block #132,677

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2013, 2:02:40 AM Β· Difficulty 9.7895 Β· 6,684,068 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
68f0e3cabb46c475509f236ea80cf7a41bf323f6b9fefe2b9f6d8d7afc0e17be
View on Chainz β†—

Height

#132,677

Difficulty

9.789495

Transactions

1

Size

197 B

Version

2

Bits

09ca1c5f

Nonce

398,720

Timestamp

8/25/2013, 2:02:40 AM

Confirmations

6,684,068

Mined by

⛏️ P2SHAJYjKv6MiC978JMgPHsTyLZP4H8TXfzr5c

Merkle Root

b31afc2b52cca8f33ccb6a482a08fab8e93d2b1bb616eb88ad02e6b8cb352551
Transactions (1)
Coinbaseb31afc2b52cca8…02e6b8cb352551
1 in β†’ 1 out10.4200 XPM109 B
AJYjKv6M…8TXfzr5c
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.

1.766 Γ— 10⁸⁹(90-digit number)
17669633606154417788…57711065166812633559
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
1.766 Γ— 10⁸⁹(90-digit number)
17669633606154417788…57711065166812633559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.766 Γ— 10⁸⁹(90-digit number)
17669633606154417788…57711065166812633561
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
3.533 Γ— 10⁸⁹(90-digit number)
35339267212308835576…15422130333625267119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.533 Γ— 10⁸⁹(90-digit number)
35339267212308835576…15422130333625267121
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
7.067 Γ— 10⁸⁹(90-digit number)
70678534424617671152…30844260667250534239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.067 Γ— 10⁸⁹(90-digit number)
70678534424617671152…30844260667250534241
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
1.413 Γ— 10⁹⁰(91-digit number)
14135706884923534230…61688521334501068479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.413 Γ— 10⁹⁰(91-digit number)
14135706884923534230…61688521334501068481
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
2.827 Γ— 10⁹⁰(91-digit number)
28271413769847068460…23377042669002136959
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:57,777,997 XPMΒ·at block #6,816,744 Β· updates every 60s
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