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Block #440,463

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/12/2014, 10:48:00 AM Β· Difficulty 10.3528 Β· 6,366,408 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
55238025a00cb6ae62df6369fa203791d74083c33c03208f9fb8297349b54a0b
View on Chainz β†—

Height

#440,463

Difficulty

10.352798

Transactions

1

Size

207 B

Version

2

Bits

0a5a50fe

Nonce

7,423

Timestamp

3/12/2014, 10:48:00 AM

Confirmations

6,366,408

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

21de29534012df6173226fafb34d6f95cbfa8680ca34f59f0b7dd83450b18ae2
Transactions (1)
Coinbase21de29534012df…7dd83450b18ae2
1 in β†’ 1 out9.3200 XPM116 B
AbwWkWZt…kawDhufa
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.

2.171 Γ— 10⁹⁢(97-digit number)
21712065775842793244…79665760914951445279
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
2.171 Γ— 10⁹⁢(97-digit number)
21712065775842793244…79665760914951445279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.171 Γ— 10⁹⁢(97-digit number)
21712065775842793244…79665760914951445281
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
4.342 Γ— 10⁹⁢(97-digit number)
43424131551685586488…59331521829902890559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.342 Γ— 10⁹⁢(97-digit number)
43424131551685586488…59331521829902890561
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
8.684 Γ— 10⁹⁢(97-digit number)
86848263103371172977…18663043659805781119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.684 Γ— 10⁹⁢(97-digit number)
86848263103371172977…18663043659805781121
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
1.736 Γ— 10⁹⁷(98-digit number)
17369652620674234595…37326087319611562239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.736 Γ— 10⁹⁷(98-digit number)
17369652620674234595…37326087319611562241
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
3.473 Γ— 10⁹⁷(98-digit number)
34739305241348469191…74652174639223124479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.473 Γ— 10⁹⁷(98-digit number)
34739305241348469191…74652174639223124481
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:57,699,075 XPMΒ·at block #6,806,870 Β· updates every 60s
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