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Block #27,822

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 10:10:51 AM Β· Difficulty 7.9801 Β· 6,772,767 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4865ef633e7689111ffa126af0d8fb557da25a292fcf281c03893625166eadd5
View on Chainz β†—

Height

#27,822

Difficulty

7.980063

Transactions

1

Size

199 B

Version

2

Bits

07fae568

Nonce

367

Timestamp

7/13/2013, 10:10:51 AM

Confirmations

6,772,767

Mined by

⛏️ P2SHAKSwr9eUsXtYAeGKZ6MmF96jvsdLNxuVyn

Merkle Root

ffb1b3e6c6584224ad0e2e630f4e7118fbaaf40efc9c9ba31f90d1b63282712c
Transactions (1)
Coinbaseffb1b3e6c65842…90d1b63282712c
1 in β†’ 1 out15.6800 XPM108 B
AKSwr9eU…dLNxuVyn
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.

1.555 Γ— 10⁹⁢(97-digit number)
15556525209832544961…59971576805834604939
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
1.555 Γ— 10⁹⁢(97-digit number)
15556525209832544961…59971576805834604939
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.555 Γ— 10⁹⁢(97-digit number)
15556525209832544961…59971576805834604941
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
3.111 Γ— 10⁹⁢(97-digit number)
31113050419665089922…19943153611669209879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.111 Γ— 10⁹⁢(97-digit number)
31113050419665089922…19943153611669209881
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
6.222 Γ— 10⁹⁢(97-digit number)
62226100839330179845…39886307223338419759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.222 Γ— 10⁹⁢(97-digit number)
62226100839330179845…39886307223338419761
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
1.244 Γ— 10⁹⁷(98-digit number)
12445220167866035969…79772614446676839519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,648,771 XPMΒ·at block #6,800,588 Β· updates every 60s
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