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Block #27,966

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 10:42:18 AM Β· Difficulty 7.9805 Β· 6,780,976 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
663f9eefb85a2548501e9486e6215a639eed5d2d46dfea6929a65107a12db02b
View on Chainz β†—

Height

#27,966

Difficulty

7.980506

Transactions

1

Size

199 B

Version

2

Bits

07fb0270

Nonce

171

Timestamp

7/13/2013, 10:42:18 AM

Confirmations

6,780,976

Mined by

⛏️ P2SHAV6P7enUMtWL6sjxBf1aCsLJbsVLHeixvR

Merkle Root

2e58eea95d77c773a853427bf01c6ddef61d91b30e01e0fa77098b9871cb9c42
Transactions (1)
Coinbase2e58eea95d77c7…098b9871cb9c42
1 in β†’ 1 out15.6800 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.

2.651 Γ— 10⁹⁢(97-digit number)
26512560487598841531…17715578469812107679
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
2.651 Γ— 10⁹⁢(97-digit number)
26512560487598841531…17715578469812107679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.651 Γ— 10⁹⁢(97-digit number)
26512560487598841531…17715578469812107681
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
5.302 Γ— 10⁹⁢(97-digit number)
53025120975197683062…35431156939624215359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.302 Γ— 10⁹⁢(97-digit number)
53025120975197683062…35431156939624215361
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
1.060 Γ— 10⁹⁷(98-digit number)
10605024195039536612…70862313879248430719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.060 Γ— 10⁹⁷(98-digit number)
10605024195039536612…70862313879248430721
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
2.121 Γ— 10⁹⁷(98-digit number)
21210048390079073224…41724627758496861439
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:57,715,594 XPMΒ·at block #6,808,941 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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