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Block #164,486

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2013, 4:55:49 PM Β· Difficulty 9.8628 Β· 6,652,109 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca43eafcade2c7521aa3dd135ca8ff7136b501b7eb816ba4462bc7ecb0bc8fd4
View on Chainz β†—

Height

#164,486

Difficulty

9.862835

Transactions

1

Size

200 B

Version

2

Bits

09dce2bb

Nonce

130,565

Timestamp

9/14/2013, 4:55:49 PM

Confirmations

6,652,109

Mined by

⛏️ P2SHAe6PYBDNs6MFPfqSfG8TyUUBAHjSQhB18y

Merkle Root

fc28d7f884cbcd948697864114ad21f71fdd02f1cd0feec0246579fe65f56c4e
Transactions (1)
Coinbasefc28d7f884cbcd…6579fe65f56c4e
1 in β†’ 1 out10.2600 XPM109 B
Ae6PYBDN…jSQhB18y
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.

1.108 Γ— 10⁹⁷(98-digit number)
11081727347411239911…76706151254794050559
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
1.108 Γ— 10⁹⁷(98-digit number)
11081727347411239911…76706151254794050559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.108 Γ— 10⁹⁷(98-digit number)
11081727347411239911…76706151254794050561
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
2.216 Γ— 10⁹⁷(98-digit number)
22163454694822479823…53412302509588101119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.216 Γ— 10⁹⁷(98-digit number)
22163454694822479823…53412302509588101121
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
4.432 Γ— 10⁹⁷(98-digit number)
44326909389644959646…06824605019176202239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.432 Γ— 10⁹⁷(98-digit number)
44326909389644959646…06824605019176202241
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
8.865 Γ— 10⁹⁷(98-digit number)
88653818779289919292…13649210038352404479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.865 Γ— 10⁹⁷(98-digit number)
88653818779289919292…13649210038352404481
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
1.773 Γ— 10⁹⁸(99-digit number)
17730763755857983858…27298420076704808959
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:57,776,885 XPMΒ·at block #6,816,594 Β· updates every 60s
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