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Block #30,972

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 9:27:40 PM Β· Difficulty 7.9879 Β· 6,776,872 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
17bcff6087c392bebd422c25e74ba344d621487f1d177b619ec43497024d1a5c
View on Chainz β†—

Height

#30,972

Difficulty

7.987869

Transactions

1

Size

200 B

Version

2

Bits

07fce4f7

Nonce

240

Timestamp

7/13/2013, 9:27:40 PM

Confirmations

6,776,872

Mined by

⛏️ P2SHAV6P7enUMtWL6sjxBf1aCsLJbsVLHeixvR

Merkle Root

6c4a90f3b064be14cb4c4f0fd820811449808e37801c627f288ef9fc32638703
Transactions (1)
Coinbase6c4a90f3b064be…8ef9fc32638703
1 in β†’ 1 out15.6500 XPM108 B
AV6P7enU…VLHeixvR
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.

8.803 Γ— 10⁹⁸(99-digit number)
88034300162939480936…16840295184254479799
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
8.803 Γ— 10⁹⁸(99-digit number)
88034300162939480936…16840295184254479799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.803 Γ— 10⁹⁸(99-digit number)
88034300162939480936…16840295184254479801
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
1.760 Γ— 10⁹⁹(100-digit number)
17606860032587896187…33680590368508959599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.760 Γ— 10⁹⁹(100-digit number)
17606860032587896187…33680590368508959601
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
3.521 Γ— 10⁹⁹(100-digit number)
35213720065175792374…67361180737017919199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.521 Γ— 10⁹⁹(100-digit number)
35213720065175792374…67361180737017919201
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
7.042 Γ— 10⁹⁹(100-digit number)
70427440130351584749…34722361474035838399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.042 Γ— 10⁹⁹(100-digit number)
70427440130351584749…34722361474035838401
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:57,706,790 XPMΒ·at block #6,807,843 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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