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Block #178,610

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/24/2013, 12:47:22 PM Β· Difficulty 9.8630 Β· 6,633,603 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c63941d78f725b3003e9e9555f1baa2e074a7f3856cefe8ec479ecf191613a0a
View on Chainz β†—

Height

#178,610

Difficulty

9.862989

Transactions

1

Size

200 B

Version

2

Bits

09dcece0

Nonce

480,260

Timestamp

9/24/2013, 12:47:22 PM

Confirmations

6,633,603

Mined by

⛏️ P2SHAVJaZtXCr3NXSK79aMri9GXJU2gGZDZ3Yk

Merkle Root

8f98207a0702b9550c9d14e70b03debb911fc615e62f08060403eb3c831cd573
Transactions (1)
Coinbase8f98207a0702b9…03eb3c831cd573
1 in β†’ 1 out10.2600 XPM109 B
AVJaZtXC…gGZDZ3Yk
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.

2.211 Γ— 10⁹⁢(97-digit number)
22117692333206236331…56047915948713246079
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
2.211 Γ— 10⁹⁢(97-digit number)
22117692333206236331…56047915948713246079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.211 Γ— 10⁹⁢(97-digit number)
22117692333206236331…56047915948713246081
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
4.423 Γ— 10⁹⁢(97-digit number)
44235384666412472662…12095831897426492159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.423 Γ— 10⁹⁢(97-digit number)
44235384666412472662…12095831897426492161
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
8.847 Γ— 10⁹⁢(97-digit number)
88470769332824945325…24191663794852984319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.847 Γ— 10⁹⁢(97-digit number)
88470769332824945325…24191663794852984321
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
1.769 Γ— 10⁹⁷(98-digit number)
17694153866564989065…48383327589705968639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.769 Γ— 10⁹⁷(98-digit number)
17694153866564989065…48383327589705968641
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
3.538 Γ— 10⁹⁷(98-digit number)
35388307733129978130…96766655179411937279
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:57,741,717 XPMΒ·at block #6,812,212 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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