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Block #14,337

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/11/2013, 4:15:11 PM Β· Difficulty 7.8228 Β· 6,800,692 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ddc7f98e74413f0bdbb3a8312175c5fbbfd858c2b515b07bf9a004ba218aa663
View on Chainz β†—

Height

#14,337

Difficulty

7.822781

Transactions

1

Size

202 B

Version

2

Bits

07d2a1c0

Nonce

615

Timestamp

7/11/2013, 4:15:11 PM

Confirmations

6,800,692

Mined by

⛏️ P2SHAJbz55M2Xd4eSVXFrry1sb6y1EmoHxsz79

Merkle Root

24f58ddd2fc9177963d07f2b3845cdb4ed497a1c0c28417287087811b1cef5db
Transactions (1)
Coinbase24f58ddd2fc917…087811b1cef5db
1 in β†’ 1 out16.3200 XPM108 B
AJbz55M2…moHxsz79
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.

3.888 Γ— 10¹⁰⁡(106-digit number)
38887961438953106367…46100179595660368239
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
3.888 Γ— 10¹⁰⁡(106-digit number)
38887961438953106367…46100179595660368239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.888 Γ— 10¹⁰⁡(106-digit number)
38887961438953106367…46100179595660368241
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
7.777 Γ— 10¹⁰⁡(106-digit number)
77775922877906212735…92200359191320736479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.777 Γ— 10¹⁰⁡(106-digit number)
77775922877906212735…92200359191320736481
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
1.555 Γ— 10¹⁰⁢(107-digit number)
15555184575581242547…84400718382641472959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.555 Γ— 10¹⁰⁢(107-digit number)
15555184575581242547…84400718382641472961
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
3.111 Γ— 10¹⁰⁢(107-digit number)
31110369151162485094…68801436765282945919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.111 Γ— 10¹⁰⁢(107-digit number)
31110369151162485094…68801436765282945921
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:57,764,321 XPMΒ·at block #6,815,028 Β· updates every 60s
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