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Block #378,752

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/28/2014, 2:01:00 AM Β· Difficulty 10.4149 Β· 6,437,103 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a5007bd86eb086017117199a78aaa459d7c0ee367bb9733d5782c682f38a4280
View on Chainz β†—

Height

#378,752

Difficulty

10.414886

Transactions

2

Size

428 B

Version

2

Bits

0a6a35fe

Nonce

112,361

Timestamp

1/28/2014, 2:01:00 AM

Confirmations

6,437,103

Mined by

⛏️ P2SHARjv1564C2eTPyhc6wiYTUxeobTwg8Ms63

Merkle Root

243ede30cb3c0916fcc3f6defbc88ab7a8657193e797de237aa4fd784d332871
Transactions (2)
Coinbase7205373cf1bdf1…a0c5035130e703
1 in β†’ 1 out9.2100 XPM111 B
ARjv1564…Twg8Ms63
cf7b017d54b33e…009a0c8fab097a
1 in β†’ 2 out5.0786 XPM226 B
AYmfF1Y9…ry5iPAxHAbWZ2nJi…5Li7Fd5t
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.

4.062 Γ— 10⁹⁢(97-digit number)
40629128884782655723…70827158912472334079
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
4.062 Γ— 10⁹⁢(97-digit number)
40629128884782655723…70827158912472334079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.062 Γ— 10⁹⁢(97-digit number)
40629128884782655723…70827158912472334081
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
8.125 Γ— 10⁹⁢(97-digit number)
81258257769565311447…41654317824944668159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.125 Γ— 10⁹⁢(97-digit number)
81258257769565311447…41654317824944668161
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
1.625 Γ— 10⁹⁷(98-digit number)
16251651553913062289…83308635649889336319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.625 Γ— 10⁹⁷(98-digit number)
16251651553913062289…83308635649889336321
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
3.250 Γ— 10⁹⁷(98-digit number)
32503303107826124579…66617271299778672639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.250 Γ— 10⁹⁷(98-digit number)
32503303107826124579…66617271299778672641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
6.500 Γ— 10⁹⁷(98-digit number)
65006606215652249158…33234542599557345279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.500 Γ— 10⁹⁷(98-digit number)
65006606215652249158…33234542599557345281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,770,951 XPMΒ·at block #6,815,854 Β· updates every 60s
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