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Block #179,095

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/24/2013, 8:16:15 PM Β· Difficulty 9.8639 Β· 6,624,652 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
055ac7735f6d274b5cb5dbdb08c07693910cf2d5ff22c57bdbf0442e422bdeb0
View on Chainz β†—

Height

#179,095

Difficulty

9.863945

Transactions

2

Size

1.29 KB

Version

2

Bits

09dd2b7f

Nonce

172,452

Timestamp

9/24/2013, 8:16:15 PM

Confirmations

6,624,652

Mined by

⛏️ P2SHAP1gyZXxfrBjGDz3MkjK6fwMgGuWqJpvNn

Merkle Root

f6a67faa53ac95304c13571a6b865643a691030899cf674cd7844af3ca7d34c5
Transactions (2)
Coinbase31b6c5ca8d6d3b…e1746d7f9c57b8
1 in β†’ 1 out10.2831 XPM109 B
AP1gyZXx…uWqJpvNn
064b2758d4210e…3f55a0943a0f3d
8 in β†’ 1 out51.1900 XPM1.10 KB
AYGvdd1X…t4pDQkC5
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.

5.743 Γ— 10⁹³(94-digit number)
57438031845743482605…31179842705703461399
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
5.743 Γ— 10⁹³(94-digit number)
57438031845743482605…31179842705703461399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.743 Γ— 10⁹³(94-digit number)
57438031845743482605…31179842705703461401
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
1.148 Γ— 10⁹⁴(95-digit number)
11487606369148696521…62359685411406922799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.148 Γ— 10⁹⁴(95-digit number)
11487606369148696521…62359685411406922801
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
2.297 Γ— 10⁹⁴(95-digit number)
22975212738297393042…24719370822813845599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.297 Γ— 10⁹⁴(95-digit number)
22975212738297393042…24719370822813845601
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
4.595 Γ— 10⁹⁴(95-digit number)
45950425476594786084…49438741645627691199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.595 Γ— 10⁹⁴(95-digit number)
45950425476594786084…49438741645627691201
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
9.190 Γ— 10⁹⁴(95-digit number)
91900850953189572169…98877483291255382399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.190 Γ— 10⁹⁴(95-digit number)
91900850953189572169…98877483291255382401
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:57,674,014 XPMΒ·at block #6,803,746 Β· updates every 60s
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