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Block #132,901

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2013, 5:25:47 AM Β· Difficulty 9.7904 Β· 6,681,116 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9d8d692c27c6e3325d5830a92ac3a1f2995d82afcb436c257cc03660f0957f34
View on Chainz β†—

Height

#132,901

Difficulty

9.790356

Transactions

1

Size

200 B

Version

2

Bits

09ca54bf

Nonce

41,235

Timestamp

8/25/2013, 5:25:47 AM

Confirmations

6,681,116

Mined by

⛏️ P2SHAY88KHSTJpyaPqTYGEt3LWdPpt88L8yacq

Merkle Root

85ee7e55429560010f792e307822837c6957f1a37fe29a9e7ad55237e4f9e465
Transactions (1)
Coinbase85ee7e55429560…d55237e4f9e465
1 in β†’ 1 out10.4200 XPM109 B
AY88KHST…88L8yacq
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.

1.704 Γ— 10⁹⁸(99-digit number)
17046391466946474836…66866513551038110559
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
1.704 Γ— 10⁹⁸(99-digit number)
17046391466946474836…66866513551038110559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.704 Γ— 10⁹⁸(99-digit number)
17046391466946474836…66866513551038110561
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
3.409 Γ— 10⁹⁸(99-digit number)
34092782933892949673…33733027102076221119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.409 Γ— 10⁹⁸(99-digit number)
34092782933892949673…33733027102076221121
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
6.818 Γ— 10⁹⁸(99-digit number)
68185565867785899346…67466054204152442239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.818 Γ— 10⁹⁸(99-digit number)
68185565867785899346…67466054204152442241
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
1.363 Γ— 10⁹⁹(100-digit number)
13637113173557179869…34932108408304884479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.363 Γ— 10⁹⁹(100-digit number)
13637113173557179869…34932108408304884481
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
2.727 Γ— 10⁹⁹(100-digit number)
27274226347114359738…69864216816609768959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.727 Γ— 10⁹⁹(100-digit number)
27274226347114359738…69864216816609768961
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
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