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Block #175,255

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/22/2013, 4:19:06 AM Β· Difficulty 9.8636 Β· 6,633,646 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aba9a51bc9af1a380a391c6f1a2b8cbd90095a5fb08469dfeb9b40e87decfcb6
View on Chainz β†—

Height

#175,255

Difficulty

9.863627

Transactions

1

Size

199 B

Version

2

Bits

09dd16b0

Nonce

2,953

Timestamp

9/22/2013, 4:19:06 AM

Confirmations

6,633,646

Mined by

⛏️ P2SHAJQ7bqzh8jMKwbhminzZ7vurTxoY2ANRaW

Merkle Root

b01aa6808ad994260ae202cc2f94aef2748cac16c5e1d8f5e49fc5940b16b8d3
Transactions (1)
Coinbaseb01aa6808ad994…9fc5940b16b8d3
1 in β†’ 1 out10.2600 XPM109 B
AJQ7bqzh…oY2ANRaW
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.

3.387 Γ— 10⁹⁡(96-digit number)
33870473770406171501…64075401214043750399
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
3.387 Γ— 10⁹⁡(96-digit number)
33870473770406171501…64075401214043750399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.387 Γ— 10⁹⁡(96-digit number)
33870473770406171501…64075401214043750401
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
6.774 Γ— 10⁹⁡(96-digit number)
67740947540812343002…28150802428087500799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.774 Γ— 10⁹⁡(96-digit number)
67740947540812343002…28150802428087500801
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
1.354 Γ— 10⁹⁢(97-digit number)
13548189508162468600…56301604856175001599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.354 Γ— 10⁹⁢(97-digit number)
13548189508162468600…56301604856175001601
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
2.709 Γ— 10⁹⁢(97-digit number)
27096379016324937201…12603209712350003199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.709 Γ— 10⁹⁢(97-digit number)
27096379016324937201…12603209712350003201
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
5.419 Γ— 10⁹⁢(97-digit number)
54192758032649874402…25206419424700006399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.419 Γ— 10⁹⁢(97-digit number)
54192758032649874402…25206419424700006401
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:57,715,261 XPMΒ·at block #6,808,900 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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