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Block #31,024

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 9:42:30 PM Β· Difficulty 7.9880 Β· 6,777,192 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9c432197da75344f6a3f5e02ad5a1ce0f0c3f59b86cbe67911667c872bb39909
View on Chainz β†—

Height

#31,024

Difficulty

7.987960

Transactions

1

Size

200 B

Version

2

Bits

07fceaef

Nonce

429

Timestamp

7/13/2013, 9:42:30 PM

Confirmations

6,777,192

Mined by

⛏️ P2SHAV6P7enUMtWL6sjxBf1aCsLJbsVLHeixvR

Merkle Root

1d81ac05f87e4fcd2e15e049220a1708226303263675db2029348f5622e47483
Transactions (1)
Coinbase1d81ac05f87e4f…348f5622e47483
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.

7.724 Γ— 10⁹⁹(100-digit number)
77247899695806120505…01078938674665425839
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
7.724 Γ— 10⁹⁹(100-digit number)
77247899695806120505…01078938674665425839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.724 Γ— 10⁹⁹(100-digit number)
77247899695806120505…01078938674665425841
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
1.544 Γ— 10¹⁰⁰(101-digit number)
15449579939161224101…02157877349330851679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.544 Γ— 10¹⁰⁰(101-digit number)
15449579939161224101…02157877349330851681
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
3.089 Γ— 10¹⁰⁰(101-digit number)
30899159878322448202…04315754698661703359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.089 Γ— 10¹⁰⁰(101-digit number)
30899159878322448202…04315754698661703361
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
6.179 Γ— 10¹⁰⁰(101-digit number)
61798319756644896404…08631509397323406719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.179 Γ— 10¹⁰⁰(101-digit number)
61798319756644896404…08631509397323406721
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:57,709,780 XPMΒ·at block #6,808,215 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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