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Block #24,885

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 12:25:11 AM Β· Difficulty 7.9681 Β· 6,785,620 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3281c0cfad03b97f8594f063855b492b0e0fd0338773bbb17776c8c27269c302
View on Chainz β†—

Height

#24,885

Difficulty

7.968099

Transactions

1

Size

200 B

Version

2

Bits

07f7d55a

Nonce

541

Timestamp

7/13/2013, 12:25:11 AM

Confirmations

6,785,620

Mined by

⛏️ P2SHAFt1giaBxBFiqnHUp2a6D9n9RgqjgZEnas

Merkle Root

6e9167542a6712a5934e20a8c47753e9cb9b816754810288cec5eca7320e72c2
Transactions (1)
Coinbase6e9167542a6712…c5eca7320e72c2
1 in β†’ 1 out15.7300 XPM108 B
AFt1giaB…qjgZEnas
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.

2.031 Γ— 10⁹⁸(99-digit number)
20315213391202337366…99277709563785864199
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
2.031 Γ— 10⁹⁸(99-digit number)
20315213391202337366…99277709563785864199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.031 Γ— 10⁹⁸(99-digit number)
20315213391202337366…99277709563785864201
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
4.063 Γ— 10⁹⁸(99-digit number)
40630426782404674732…98555419127571728399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.063 Γ— 10⁹⁸(99-digit number)
40630426782404674732…98555419127571728401
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
8.126 Γ— 10⁹⁸(99-digit number)
81260853564809349465…97110838255143456799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.126 Γ— 10⁹⁸(99-digit number)
81260853564809349465…97110838255143456801
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
1.625 Γ— 10⁹⁹(100-digit number)
16252170712961869893…94221676510286913599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.625 Γ— 10⁹⁹(100-digit number)
16252170712961869893…94221676510286913601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,728,123 XPMΒ·at block #6,810,504 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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