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Block #179,141

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/24/2013, 9:14:07 PM Β· Difficulty 9.8636 Β· 6,629,813 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
21776bc80e10e84c8d6af824eb0edd1cdd3da9a1d88036a1ed0bd3ce37830a14
View on Chainz β†—

Height

#179,141

Difficulty

9.863579

Transactions

2

Size

424 B

Version

2

Bits

09dd1387

Nonce

105,287

Timestamp

9/24/2013, 9:14:07 PM

Confirmations

6,629,813

Mined by

⛏️ P2SHAYdbNV3Kq2oVBRLGZsE3t5cQmmMDYUq4uV

Merkle Root

1b6153d0b56e6007f63017f392cb23a49dbdd844ce757bdf08e7921f1e23d9d8
Transactions (2)
Coinbase8a36cf74407c92…8bedb25673b03f
1 in β†’ 1 out10.2700 XPM109 B
AYdbNV3K…MDYUq4uV
26703a33233540…6dcd2754fda945
1 in β†’ 2 out10.2500 XPM225 B
AH3dDrPX…iXBYe8ZVAKpCYEg1…QiDRQ6Gc
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.

1.785 Γ— 10⁹⁡(96-digit number)
17858960615381536963…53015506032573335039
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
1.785 Γ— 10⁹⁡(96-digit number)
17858960615381536963…53015506032573335039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.785 Γ— 10⁹⁡(96-digit number)
17858960615381536963…53015506032573335041
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
3.571 Γ— 10⁹⁡(96-digit number)
35717921230763073926…06031012065146670079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.571 Γ— 10⁹⁡(96-digit number)
35717921230763073926…06031012065146670081
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
7.143 Γ— 10⁹⁡(96-digit number)
71435842461526147853…12062024130293340159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.143 Γ— 10⁹⁡(96-digit number)
71435842461526147853…12062024130293340161
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
1.428 Γ— 10⁹⁢(97-digit number)
14287168492305229570…24124048260586680319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.428 Γ— 10⁹⁢(97-digit number)
14287168492305229570…24124048260586680321
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
2.857 Γ— 10⁹⁢(97-digit number)
28574336984610459141…48248096521173360639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.857 Γ— 10⁹⁢(97-digit number)
28574336984610459141…48248096521173360641
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
Circulating Supply:57,715,685 XPMΒ·at block #6,808,953 Β· updates every 60s
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