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Block #185,167

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/29/2013, 2:58:24 AM Β· Difficulty 9.8622 Β· 6,625,403 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
238793a5bf4b2a6b1877627810721d46caae2b453d2f821f2f43ee3b88bbd99b
View on Chainz β†—

Height

#185,167

Difficulty

9.862248

Transactions

1

Size

200 B

Version

2

Bits

09dcbc50

Nonce

18,371

Timestamp

9/29/2013, 2:58:24 AM

Confirmations

6,625,403

Mined by

⛏️ P2SHAJgHpa8bWXAnCbvBMmWEijC8R51N2Bhnd4

Merkle Root

b8ba10cb8bf4ea4e88874ae61bfc171ff589bd3db94f56120480e916623c1831
Transactions (1)
Coinbaseb8ba10cb8bf4ea…80e916623c1831
1 in β†’ 1 out10.2700 XPM109 B
AJgHpa8b…1N2Bhnd4
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.

2.334 Γ— 10⁹⁢(97-digit number)
23340356941220946394…80667210115317657599
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
2.334 Γ— 10⁹⁢(97-digit number)
23340356941220946394…80667210115317657599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.334 Γ— 10⁹⁢(97-digit number)
23340356941220946394…80667210115317657601
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
4.668 Γ— 10⁹⁢(97-digit number)
46680713882441892789…61334420230635315199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.668 Γ— 10⁹⁢(97-digit number)
46680713882441892789…61334420230635315201
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
9.336 Γ— 10⁹⁢(97-digit number)
93361427764883785579…22668840461270630399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.336 Γ— 10⁹⁢(97-digit number)
93361427764883785579…22668840461270630401
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
1.867 Γ— 10⁹⁷(98-digit number)
18672285552976757115…45337680922541260799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.867 Γ— 10⁹⁷(98-digit number)
18672285552976757115…45337680922541260801
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
3.734 Γ— 10⁹⁷(98-digit number)
37344571105953514231…90675361845082521599
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:57,728,651 XPMΒ·at block #6,810,569 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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