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Block #176,849

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/23/2013, 5:56:53 AM Β· Difficulty 9.8652 Β· 6,640,320 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5cd1df963117ff9366213b534dc9f2bd0840c875d2b86cb9720fa0f5152dc3fc
View on Chainz β†—

Height

#176,849

Difficulty

9.865249

Transactions

1

Size

199 B

Version

2

Bits

09dd80f4

Nonce

49,267

Timestamp

9/23/2013, 5:56:53 AM

Confirmations

6,640,320

Mined by

⛏️ P2SHAHNdTz9RdyhMpsaRttP7HwiXvgDHU2jpcA

Merkle Root

1bd70d4237ce39730d96f4a0a90955aa550cf92e3d31ec71ba90c51630ad038f
Transactions (1)
Coinbase1bd70d4237ce39…90c51630ad038f
1 in β†’ 1 out10.2600 XPM109 B
AHNdTz9R…DHU2jpcA
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.

5.488 Γ— 10⁹⁡(96-digit number)
54887064932519243474…04258434674888873839
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
5.488 Γ— 10⁹⁡(96-digit number)
54887064932519243474…04258434674888873839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.488 Γ— 10⁹⁡(96-digit number)
54887064932519243474…04258434674888873841
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
1.097 Γ— 10⁹⁢(97-digit number)
10977412986503848694…08516869349777747679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.097 Γ— 10⁹⁢(97-digit number)
10977412986503848694…08516869349777747681
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
2.195 Γ— 10⁹⁢(97-digit number)
21954825973007697389…17033738699555495359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.195 Γ— 10⁹⁢(97-digit number)
21954825973007697389…17033738699555495361
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
4.390 Γ— 10⁹⁢(97-digit number)
43909651946015394779…34067477399110990719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.390 Γ— 10⁹⁢(97-digit number)
43909651946015394779…34067477399110990721
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
8.781 Γ— 10⁹⁢(97-digit number)
87819303892030789558…68134954798221981439
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:57,781,387 XPMΒ·at block #6,817,168 Β· updates every 60s
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