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Block #179,754

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/25/2013, 8:04:27 AM Β· Difficulty 9.8627 Β· 6,616,237 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa856221569a6f9700f694f7d5e6b9d8c19fe6414e21098a874ea8fd965991a6
View on Chainz β†—

Height

#179,754

Difficulty

9.862655

Transactions

2

Size

4.66 KB

Version

2

Bits

09dcd6f3

Nonce

61,477

Timestamp

9/25/2013, 8:04:27 AM

Confirmations

6,616,237

Mined by

⛏️ P2SHANuF339wP4ayd5BSmDmS68NREGiYPZq6Rh

Merkle Root

98c6384e9b06031e8d7d9a3230d45a5126cd78e04d71ff6124ee25eb4ba05b71
Transactions (2)
Coinbase061d4f7d305b13…685f2bff9a8f9a
1 in β†’ 1 out10.3200 XPM109 B
ANuF339w…iYPZq6Rh
4a34626c4879c7…5b4ca58bcce121
37 in β†’ 1 out290.9518 XPM4.46 KB
Acd1BgN5…bE5c9NoN
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.

1.690 Γ— 10⁹⁸(99-digit number)
16904337072892460740…64230799926754475519
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
1.690 Γ— 10⁹⁸(99-digit number)
16904337072892460740…64230799926754475519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.690 Γ— 10⁹⁸(99-digit number)
16904337072892460740…64230799926754475521
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
3.380 Γ— 10⁹⁸(99-digit number)
33808674145784921480…28461599853508951039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.380 Γ— 10⁹⁸(99-digit number)
33808674145784921480…28461599853508951041
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
6.761 Γ— 10⁹⁸(99-digit number)
67617348291569842961…56923199707017902079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.761 Γ— 10⁹⁸(99-digit number)
67617348291569842961…56923199707017902081
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
1.352 Γ— 10⁹⁹(100-digit number)
13523469658313968592…13846399414035804159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.352 Γ— 10⁹⁹(100-digit number)
13523469658313968592…13846399414035804161
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
2.704 Γ— 10⁹⁹(100-digit number)
27046939316627937184…27692798828071608319
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:57,612,024 XPMΒ·at block #6,795,990 Β· updates every 60s
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